to do a PSA = to do a public service announcement = [to perform in / to appear in / to speak in] a public service announcement. A public service announcement is like a television advertisement, but its purpose is to inform the public rather than to sell products. do a PSA becomes simply do PSA because articles are frequently omitted in headlines.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.