Adjunct professor capacities
The easiest way to resolve this question is to e-mail the person and ask whether they anticipate taking new graduate students in the near future.  This is worth asking even for non-adjunct faculty (since they may have all the students they can handle already, they may be retiring soon or moving to another university or an administrative position, etc.), so nobody will be surprised or take offense at the question.

As for what sort of answer to expect, it depends on what sort of adjunct professor it is.  Sometimes researchers from other institutions (government or industrial research labs, museums, etc.) hold adjunct positions at universities.  They may or may not be allowed to supervise graduate students, depending on the terms of their appointment, but it's common to allow this; often it's part of the point of the position.  On the other hand, there's another sort of position sometimes called adjunct faculty, namely low-paid temporary workers hired to teach introductory courses, and these jobs are not likely to involve graduate supervision.  You should be able to tell pretty easily which case applies to any particular person by looking on the web, and in any case e-mailing them (as described above) will give a definitive answer.