There are different ways to approach it, however, and I will discuss a few issues/ideas that you may want to consider when developing your approach. (I have included definitions where I felt necessary.)
Here are some general research issues:
The population for this question is undergraduate sociology students in the U.S.
Population - The population for a study is that group about whom we want to draw conclusions. We're almost never able to study all the members of the population that interests us, however, and we can never make every possible observation of them. It is just too costly and time-consuming to collect the data from all the colleges and universities in the U.S.!
How do we estimate the number?
Sampling Frame - A complete list of all the sampling elements of the population we wish to study. For example, if we want to sample voters in an upcoming election, the voters' lists represent a sampling frame of all eligible voters who have been enumerated. The availability of a sampling frame is rare, for obvious reasons.
If we could contact all the universities and colleges in the U.S., and get a complete and up-to-date list of all the students registered in sociology as their major, we would have our answer. Since this is unlikely to be accessible, we need to come up ...
This solution is a discussion of how to estimate the number of undergraduate sociology students in U.S. Definitions and procedures are detailed.