What oath did medical students take in Nazi Germany between 1933 and 1945? –– Short answer: None.

That is: practically only very, very few German doctors had to cite at least some kind of oaths, pledges, or promises of or to a 'code of professional conduct' in various formulations during ceremonies of graduation or approbation.

One difficult aspect here is that there is no The Hippocratic Oath in general, and there is absolutely no hippocratic oath now in Germany.

The Hippocratic Oath is a wonderful document from the middle of the first millennium BC but after it was formulated the realities in which doctors had to 'operate' changed quite considerably. While previously the hippocratic oath was pledged before beginning the study of medicine this pledge or a variant of it was shifted in Early Modern times to the end of the studies. And while the graduation ceremony always included some kind of oath, in American faculties for example, this was and is just optional in some in Germany. Today, no-one has to swear it in Germany. This is now a Gelöbnis attached to the Berufsordnung. This started to be codified during the 1920s and formally adopted into law through the Reichsärtzekammer under Nazi rule. While that is still intended to be in the same spirit it is also devoid of many aspects of the difficult to translate original and only formulated as a promise, not an oath. Further it is only a recommendation, like it always was since the days of the Reichsärztekammer that is now the Bundesärztekammer.

We might also remind us that today, many doctors violate the original oath routinely – either in practice or in discussions meant to adapt "the oath" to modern times.

The original in full:

I swear by Apollo the Healer, by Asclepius, by Hygieia, by Panacea, and by all the gods and goddesses, making them my witnesses, that I will carry out, according to my ability and judgment, this oath and this indenture.

To hold my teacher in this art equal to my own parents; to make him partner in my livelihood; when he is in need of money to share mine with him; to consider his family as my own brothers, and to teach them this art, if they want to learn it, without fee or indenture; to impart precept, oral instruction, and all other instruction to my own sons, the sons of my teacher, and to indentured pupils who have taken the physician’s oath, but to nobody else.

I will use treatment to help the sick according to my ability and judgment, but never with a view to injury and wrong-doing. Neither will I administer a poison to anybody when asked to do so, nor will I suggest such a course. Similarly I will not give to a woman a pessary to cause abortion. But I will keep pure and holy both my life and my art. I will not use the knife, not even, verily, on sufferers from stone, but I will give place to such as are craftsmen therein.

Into whatsoever houses I enter, I will enter to help the sick, and I will abstain from all intentional wrong-doing and harm, especially from abusing the bodies of man or woman, bond or free. And whatsoever I shall see or hear in the course of my profession, as well as outside my profession in my intercourse with men, if it be what should not be published abroad, I will never divulge, holding such things to be holy secrets.

Now if I carry out this oath, and break it not, may I gain for ever reputation among all men for my life and for my art; but if I break it and forswear myself, may the opposite befall me.6
_{- Translation by James Loeb. (Alternative version)}

The short original calls (1) for respect and faith in pagan gods, (2) expressly forbids abortions, and (4) assisted dying, (5) operations, not even on bladder stones, (6) calls for secrecy regarding the methods of the trade and also (7) forbids study fees.

This makes it difficult to follow or invalid from the start for Jews, Christians and Moslems at least.

Above all, "it" is really outdated and open for interpretation. To illustrate that with a quote from sempaiscuba's answer:

A famous case, and one that is frequently cited to illustrate this point, is that of Dr Fritz Klein who is recorded as having said:

“My Hippocratic oath tells me to cut a gangrenous appendix out of the human body. The Jews are the gangrenous appendix of mankind. That’s why I cut them out.”

Whether or not that quote is accurate: It really was 'his' hippocratic oath, since the original would have forbidden him (6) to even do that kind of thing to a single individual, lest a whole Volkskörper, or "human kind": "I will not use the knife, not even, verily, on sufferers from stone, but I will give place to such as are craftsmen therein."

A discussion about "the hippokratic oath" is therefore quite difficult in general, and especially fruitless in judging ethics and morals of German doctors in Nazi times.

Even the apparently most unquestionable principle codified in "the oath" –– First: Do no Harm! –– is always a judgement call; and thus subject to opinion and reigning ethics. Using a knife on a patient always does harm. It is sometimes better for the survival of the patient – or a patient as a whole – to amputate. Seeing a slight shift in interpreting this principle among German doctors when they start to fantasise about public health, race hygiene, eugenics is not difficult. (Although despicable and even scientifically counterproductive, to be sure.)

So, while these principles derived from the oath were and are always subject to debate, what do we know about the relationship German doctors had with "the oath"?

From the doctor's trial at Nuremberg:

Just three of the accused doctors had parents who were physicians: Gebhardt, Mrugowsky and Beiglböck. Mrugowsky’s father had been killed in military action in 1914, and Gebhardt’s father (a Bavarian public health official and a friend of the Himmlers), and Beiglböck’s father (an Austrian country doctor) were nationalist activists. These cases show how a nationalist outlook was radicalised by the next generation. Most of those on trial did not come from traditional medical elite families, and lacked the socialisation of growing up in a medical family, from which they could have derived an ethical understanding of the patient.
Sievers was the sole accused who did not hold a university degree. He had worked in publishing, which was a respected para-academic career, and through this had come to administer the SS research organisation. The accused doctors attended every German university, with the exception of Königsberg in East Prussia. Some spent semesters in Innsbruck. Pokorny had studied from 1917 to 1922 at the German University in Prague, and had been assistant at the clinic for skin and venereal diseases in 1922–4. The accused were products of the German university-based system of medical education with its values geared to the experimental basis of medicine. While some had scruples regarding the ethics of human experiments, none could remember ever having sworn anything like the Hippocratic Oath.
_{Paul Julian Weindling: "Nazi Medicine and the Nuremberg Trials. From Medical War Crimes to Informed Consent", Palgrave Macmillan: London, 2004. (p175)}

A problem remaining is that the Germans still subscribed to the tradition of acting according to "the oath", or at least its principles, now clashing with other opinions:

Hardy, recently returned from the ISC meeting, showed its effect when he confronted the Buchenwald camp doctor Hoven with the implications of the Hippocratic Oath on 22 October 1946:

Q. When you became a doctor and were given your degree you took the oath of Hippocrates. You stated when you took that oath that you would do everything in your power to preserve life.
A. Yes
Q. Doctor you breached that oath. You may have breached the oath because of orders from above but, nevertheless, you breached the oath of a doctor. The medical profession in Germany, as you know has sunk to a depth that is disgraceful, not only to you as a German doctor, but to American doctors and doctors of other nations. It is something which will take a thousand years to wipe out. The medical profession in Germany has done things that have never been heard of before ... In this trial we are going to bring it to light so it will never happen again, so that other men so sincere in their profession won’t allow such a thing as the German Reich to destroy their belief.

We have to note that exactly parallel to war crimes the judgement of medical ethics was at rockbottom in the mid 40s but hit a high point around the Nuremberg Trials that both enjoyed to around the 1960s from when they came under sustained and successful attacks by utilitarians again.

_{(Cf Michael H. Kater: "Medizin und Mediziner im Dritten Reich. Eine Bestandsaufnahme", Historische Zeitschrift, Vol 244, 1987, p 299–352.)}

Since the Renaissance and repeated turns "back to Hippocrates" the oath has again and again been regarded as the supposed key document of ancient, i.e. Hippocratic medical ethics. Until the 20th century this led to the conclusion that the oath was a timelessly valid code of medical ethics. The enigmatic language of the text has allowed every epoch and every medical deontology since late antiquity to reflect their own standards and ideas into the oath and thus to lend them the authority of the "Father of Occidental Medicine". Since early modern times, set pieces of the oath have been incorporated into the doctoral silk and faculty statutes of medical universities (Wittenberg 1508, Basel 1570). As an oath for medical graduates, the complete text of the oath was first recited in 1804 in (post-revolutionary) Montpellier. In the 20th century, a modernised oath also belonged to the steadfast inventory of doctoral ceremonies at numerous medical schools, especially American ones.

In the medical-ethical debate of earlier years, an emblematic use of the oath has often been observed, in that not the text itself was quoted to support one's own standpoint, but only the "trademark" oath was cited (pattern: "Already the Hippocratic oath commands…"). Of course, the oath was not up to the test of the example: the prosecution and judges in the Nuremberg medical trial, who first tried to use the oath as a yardstick for the medical crimes of Nazi physicians, failed to do so, especially since some of the accused also invoked the oath. In the Geneva vow (1948) of the World Medical Association, of course, the 'Hippocratic tradition' is once again the point of reference for medical ethics with a universal claim. In the current debate on medical ethics, however, the oath hardly plays a role, since it is assigned to a "paternalistic" epoch that was believed to have been overcome, with which modern medical ethics impressively underscores its ahistorical position. However, the history of the reception of the oath uniquely reflects the self-image and external image of the medical profession and is a central aspect of medical history in general.
_{Karl-Heinz Leven: "Hippokratischer Eid", p598–599. (my translation and emphasis), in: Werner E. Gerabek et al. (Eds): "Enzyklopädie der Medizingeschichte Band 2 H-N", deGruyter: Berlin, New York, 2007.}

Summary

There was no single binding document that corresponds to the Hippokratic Oath in Germany at the time. A search for "the text" will therefore not bear fruit.
For an assessment of the ethical principles guiding German doctors at the time, you would have to look at actual laws and ethics discussions in medical papers and books from the time.

To adapt Mr Churchill here: Never were so many oaths not sworn by so few so few times.