Were there any Jewish members of the Roman Senate?

Ceasar did appoint so many Gallic senators that a joke became common: "Rome is being invaded again, the Gauls are have crossed the Pomerium! Yes, they are looking for directions to the Senate House".

So, I guess it was possible for Jewish citizens to become senators.

The short answer is "We don't know of any." The longer answer is, "Probably, eventually." As noted in comments and the other (good) answer, the nature of the Senate changed substantially from the high Republic to the declining Western Empire. Considering periods in turn:

To start with (500-200 BC) the Senate was an assembly of (a) rich, (b) former magistrates (c) living in Rome. The Senate was an integral part of the Republic, a Republic which did not make a distinction between religion and public life. It was impossible to be a senator and not participate in pagan rites and practically impossible for a Jew to gain a magistracy. Additionally, there were few Jews in Rome. So we know of no Jewish Senators (either by religion or ancestry) and can judge any to be extremely unlikely.

During the last century (150-50 BC) of the Republic (which was the second century of the empire) it suffered from a string of strong men who overturned the traditional path to the Senate, simply appointing their own men. Yet the Senate was still dominated by the (rich) aristocracy and still exclusively Roman. At the same time, since this was the first time that the East was part of the Empire, Jews came to be a significant minority in Rome, both free and slave. It seems likely that there were rich Jews in Rome, but still unlikely that any were Senators. And we still know of none either by religion or descent. (It's worth noting that politics in Rome was utterly brutal by our standard -- a modern smear campaign would be considered an unattainably wholesome ideal by Roman politicians. So if a senator was known to have Jewish ancestry, it would be used against him and might have gotten into the surviving record.)

The Principate (50 BC to 200 AD), which followed the Republic, saw a radical change in the Senate. It still was for rich men, but the old aristocracy of descent had declined -- all those civil wars took a toll -- and the new aristocracy of the politically-connected rich tended to dominate the Senate. For practical purposes the Senate became more and more appointive with a smaller and smaller proportion of its members effectively inheriting the position. (But they were still all rich.)

A big change during the Principate was that the (rich) descendents of freedmen entered the Senate in numbers. IIRC, there were still few if any instances of freedmen (freed slaves) being Senators -- though they often dominated the Imperial government. A second big change was that provincials joined the Senate in large numbers. At first they were mainly the descendents of (rich) Roman families living abroad and (rich) Italians plus some (rich) members of the elite of closely allied non-Romano-Italians. (The first to join were some wealthy Gauls from areas which had been part of Rome for more than a century.)

Rome and the Senate were still resolutely pagan. As a consequence, while it is still very unlikely that any practicing Jews were Senators, it would not be terribly surprising to discover that there were a few Senators who had Jewish ancestors. (Had it been known, it would have been an impediment to their political careers, but not insurmountable. This is not because Rome had gotten warm and fuzzy, but because wealth and clout with the Emperor counted for more.)

It should be noted that ancient sources speak of Senators who were secretly Christian. It's possible, but not well attested. This is more likely than Jewish Senators, though, since being Jewish meant Eastern ancestry which was still subject to a bit of an "eww" feeling in Rome, while there were many pure-blooded Roman Christians.

As the Principate turned into the Dominate (200ish AD to 400ish AD) all bets are off. The Senate declined in power to more or less nothing -- it was little more than the city council of Rome -- and being of Senatorial rank was most important because it was an honor and had significant legal advantages. By then, Senatorial rank was actually a political disadvantage, since emperors had ceased to trust the Senate and barred Senators from many magistracies and military and governmental posts.

(The two Jewish revolts (ca. 60 AD and 130 AD) would also have made Jewish senators less likely, since Jews (even Jews long moved out of Judea) were significantly less likely to be viewed as good Romans.)

There were certainly Christian Senators by the Dominate, but still no attested Jewish Senators. OTOH, since Jews had been resident in Rome in large numbers for a couple hundred years, it seems likely that many prominent Roman families had some Jewish ancestry. (Note that the Emperor Titus (ca. 70 AD) had a Jewish lover -- Queen Berenice -- before he became Emperor. The Romans were too xenophobic for her to become Empress and he put her aside to ascend the throne, but liaisons like this were probably quite common -- and more permanent.)

And as the Western Empire fell to pieces, who knows?

Bottom line: None that we know of, but probably some of Jewish descent, though probably none who were practicing.

It seems that we know of a few late but somewhat 'probable' cases: specifically some of the vir clarissimus, like Telesinus and Cham. With ample uncertainties surrounding them and also depending a lot on definitions.

As members of the senatorial class, they seem to be a match. As 'voting in session' senate members the case gets muddier. Such a constellation of Jewish members of the senatorial class seems a bit unusual, but certainly not impossible in late antiquity.

A clarissimus vir is a title given mostly to senators, after Constantine, signifying their eventual hereditary membership to the ordo senatorius. An upper social group that expanded to several thousand families by 430.

This vir-system of the late imperial era went from the lowest, vir clarissimus, to vir spectabilis and vir illustris, to sketch it roughly.
Even later the illustris were further stratified into viri illustres, illustres magnificentissimi and illustres gloriosissimi, with the nobilissimi then being members of the imperial household itself.

This is a problem, since members of this lower stratum of vir clarissimus should still have enjoyed the privileges of that senatorial class but were themselves eventually no longer able to participate with voting rights in senatorial sessions of the curia, which were restricted to illustres and upward.

But from the bishop of Rome, Gelasius (pope from 492–496), we have a letter in which we find one Telesinus as mentioned as a vir clarissimus and Jew. That is: perhaps, as the wording isn't terribly clear, only terse.

From the year 440 onwards, only the highest rank, viri illustres, sat in the curia and were entitled to vote. Traditionally, the majority of the senators received their rank through inheritance. Since the time of the principate, sons, grandsons, and great-grandsons in the male line had been counted within the ordo senatorius by birth. Over the course of Late Antiquity, this political and social elite turned into an ever more closed circle that no longer included the real ‘policy-makers’ such as the Germanic rulers who were involved in Roman affairs throughout the 4th and 5th centuries. This development led to the further deflation of the Senate’s political power. Changes in the numbers of active Senate members also impacted its position. While the number of active senators at Rome had increased significantly (perhaps to as many as 2000) under Constantine, it had decreased substantially by the Ostrogothic period to 110 active members. […]

In fact, as in the East, only men with the rank of illustris had a seat and a voice in the Senate. Clarissimi and spectabiles were excluded from this privilege, although they might have been allowed to attend the meetings within the curia as mere listeners. […]

Not only did Jews in Ostrogothic Italy own Christian slaves, but they also at times contravened the legal and social restrictions imposed upon them in other important ways. Another example drawn from the Gelasian corpus is that of the vir clarissimus Telesinus. Gelasius wrote a letter of recommendation on behalf of Antonius, a relative of Telesinus, to another bishop named Quinigeius. In this letter Gelasius states that although Telesinus seems to be Jewish, he has

“endeavoured to prove himself to us to such an extent that we ought to rightly call him one of us”.

The Latin is ambiguous and the improbable relationship between a Roman bishop and a Jewish senator prompted Andreas Thiel, the 19th-century editor of Gelasius’ letters, to interpret it as an indication that Telesinus had converted to Christianity.

This reading is certainly conceivable although perhaps not definitive. Telesinus’ relative Antonius, who is referred to by Gelasius as frater, most likely had converted to Christianity. However, it is possible to read Gelasius’ statement about Telesinus as a backhanded compliment (he only seemed to be Jewish). Without additional evidence it is impossible to say with any degree of certainty if Telesinus was in fact a convert. Conversion was the most obvious way for Jews to gain access to professions and patronage that might otherwise be unattainable. Antonius is an excellent example of this fact. On the other hand, the existence of a Jew of senatorial rank is unusual although not unprecedented.

The "not unprecedented" is referred to in a footnote as:

A vir clarissimus and comes named Cham is known from a funerary inscription from the late 4th or early 5th century. See Chastagnol/Gagé/Leglay/Pflaum, L’Année épigraphique, p. 67. Ruggini, “Ebrei e Orientali nell’Italia”, p. 225, n. 95.

— Christine Radtki: "The Senate at Rome in Ostrogothic Italy", and Samuel Cohen: "Religious Diversity", in: Jonathan J. Arnold, M. Shane Bjornlie & Kristina Sessa (eds): "A Companion to Ostrogothic Italy", Brill’s Companions to European History, Vol 9, Brill: Leiden, Boston, 2016

The earliest example of granting this almost prerequisite honorific title for senatorial class membership to a Jewish person that definitively continued to practice his faith would be:

Until the 6th cent. the right to vote in the Senate was limited to those holding office and to the increasingly large number of honorary illustres viri (qui a patriciis et consulibus usque ad omnes illustres viros descendunt, … soli in senatu sententiam dicere possunt - Dig. 1,9,12,1, a quote from Ulpian referring to the period of its drafting).

Among those included among the illustres on an honorary basis as early as in the time of Theodosius I (died AD 395) was the Jewish Patriarch (Cod. Theod. 16,8,8 of 392); even Christian bishops were able to receive this rank.

— Gizewski, Christian (Berlin), “Illustris vir”, in: Brill’s New Pauly, Antiquity volumes edited by: Hubert Cancik and , Helmuth Schneider, English Edition by: Christine F. Salazar, Classical Tradition volumes edited by: Manfred Landfester, English Edition by: Francis G. Gentry. Consulted online on 20 December 2021 doi