The likelihood of getting an std from anal rimming is super low to it will never happen. Read this older thread in which a top guru doctor talks about rimming. https://
www.medhelp.org/posts/STDs/RECEIVE-Rimjob---Syphilis-STDs/show/1590018 (paste into your browser). In the absence of symptoms, you don't need to test but everyone who is sexually active with multiple partners should consider getting randomly tested from time to time.
I agree with GuitarRox - the chances of getting anything from rimming only is very, very slim, and I wouldn't worry about it.
Even if your partner had oral gonorrhea or chlamydia, it would be unlikely to transmit, because that resides in the throat. If they had given you oral sex on your penis, I might advise you to test, but just rimming is unlikely to transmit anything.