A casual suru-verb meaning to go out for tea/coffee (i.e., to meet at a café and chat). Often used colloquially and sometimes as an invitation.
仕事のあとで一緒にお茶する？
Want to grab a drink (tea/coffee) together after work?
久しぶりに会う友だちとカフェでお茶した。
I met an old friend and had tea/coffee at a café.
『お茶する？』と言われて、気軽に誘われたとわかった。
When they said, 'Want to get a drink?', I realized it was a casual invitation.