I am claiming my 20 year old sister who is a full time student. Can I claim the American Opportunity Tax Credit for her on my return?

Yes.  The tuition credit goes with the student's dependency. You are the only one who can claim it. This is the case whether she is a Qualifying Relative or Qualifying Child (QC) dependent.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" [QR] in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and student status test, a relationship test and a residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. The Other dependent (qualifying relative) credit is worth (up to) $500 per dependent and is non-refundable.  That is, it can only be used to reduce an actual tax liability.

A sibling must be younger than you to be a QC but not a QR.