Do I have to wear academic regalia to a student's graduation? I have been a postdoc and including occasional lecturer for the last several years. A former student just invited me to his graduation. Would someone at my career stage at an American research university typically be expected to wear academic regalia at a graduation ceremony? I have not seen any specific guidance for this.
It sounds as if you are going to be seated in the audience as guest (e.g., sitting with the family or as if you were friend or family), so just wear 'regular' clothes. It still is a very nice thing to do and to show support.

If you are seated with the faculty (in those universities which have the faculty march in with the students), then those faculty who are part of the ceremony would wear regalia. If you are sitting with the faculty, you probably wouldn't be asking your question, as it is usually arranged in advance to do so (both to make sure there are enough faculty showing up, and to help with renting the regalia for those faculty who do not have their own. And - depending on the size of the university, there will need to be a lot of instructions of where to park, where to mass up and what time to show up in order to march in.). 

If the student is asking you to 'hood' him/her (for PhD in many US universities, the advisor can come up to put the PhD hood on the candidate) then talk to the department to find out how to get included in the 'faculty' who are formally seated in the ceremony.