Are many Russians descended from Varangian Vikings?

In general, yes, sort of. First of all there are two main divisions of Russians, the Bolshoi Russky (great Russians) and the little Russians. Then beyond this there were innumerable so-called "Slavic" tribes (Pechenegs, etc etc etc). It is important to realize that the "Slavic" peoples have widely varying ethnicities and it is only language similarities that tie them together. For example, the Serbs are completely different culturally and genetically than any of the eastern slavic tribes, who are primarily Finno-Ugaric. Even among the Finno-Ugaric slavs there are big differences between the tribes that are more from Finland compared to the so-called Turkic tribes that are from the Ural mountains. A third type which is ill-defined are the swamp-based tribes, which are very ancient, dating long before the Varangians who come from the Mansurian Lakes region. There are even also the remnants of Mongolians who date from the Golden Horde days.

Anyway, getting back to the Russians. Even though the Russians (meaning the Bolshoi Russkiy, the great Russians) are described as "slavic", this is only because of their language, not because of their ethnicity which is of Scandinavian origin. Both the great Russians and little Russians came from the Baltic region and presumably invaded there from Scandinavia. Ethnically they are completely different than the Finno-Ugaric peoples. For example, great Russians have blond hair, but Finno-Ugaric people have black hair, one of many differences.

The general tradition in Russia itself, at least before the Revolution, was that the Bolshoi Russky were the "original Russians", meaning the Rus tribe itself, and were a major group of Varangians (the oath takers). They came during 400-500 A.D. The little Russians were Scandinavians who came later during the Tuetonic invasions 800 A.D. to 1200 A.D. It is difficult to verify such things because they are oral traditions. I am merely repeating what the Bolshoi Russky, or people close to them, have told me. In any case, before the Revolution there was a clear difference in physiology and culture which differentiated the two different kinds of Russians and was obvious at the time.

During the revolution the Bolshoi Russky were all killed systematically and the little Russians became assimilated into the population, so further studies of these matters is difficult.

(By the way, I hope you appreciate that I am going to have to eat downvotes to provide you this answer.)

There are two ways to answer this question, the easy way and the hard way.

The easy way is to use language as an indication of lineage. Language is probably the foremost component of a culture, so this is a valid and typical approach.

The language Russians use ("Russian") is Slavic, while the language the Varangians used was Germanic. Historically it appears that the Varangians were never much more than a ruling class in some areas (much like the Normans in England), while the vast majority of the population remained Slavic. Much like with the Normans, it didn't take many generations for the ruling classes to become culturally absorbed into the society of their subjects. After a while even the rulers' names start looking Slavic, and at some point they quit using their Germanic language altogether, with the only traces left being some loan words. Unfortunately, the study of this exact process has been relatively light, and heavily tainted by politics, but the basic facts are there. Culturally, the Russians are descendants of the Slavic Kievan Rus people, themselves the descendants of a set of eastern Slavic tribes.

The hard way would be to perform DNA tests. I personally don't think DNA is a very good way to think about descent in any but the most technical sense. For our behavior, everything that makes a people unique, you have to look to culture, and that is decidedly not carried in the DNA. But it sometimes can be useful to back up other historical and linguistic sources.

There have been some efforts on this, but mostly as it relates to individuals. I don't know of any serious effort to apply it to the Russian public at large.