Rihanna isn't letting A$AP Rocky's ongoing trial get in the way of her plans ... the singer showed up at Nobu in L.A. Wednesday night in an oversized snake print coat!

She rocked the leather coat while celebrating her cousin's birthday -- and photogs were there as she left the building with Rocky, bundling into their vehicle and taking off before the rapper's assault trial resumes this morning.

Oversized coats are in for Riri this season ... she sported a black leather one while dining at the swanky L.A. restaurant Verse with her hubby last week after one of his court appearances.

The "Diamonds" hitmaker has been spotted around the the L.A. County Superior Courthouse downtown a handful of times since Rocky's trial began in late January ... supporting him after he pleaded not guilty, rejecting a plea deal. He's charged with 2 felony counts of assault with a semiautomatic firearm ... and now faces up to 24 years in prison if convicted.

Last week she sat in the courtroom with Rocky's mother and sister. Sources with direct knowledge tell TMZ ... Rihanna is planning to appear in court today "to support her man" as A$AP's trial resumes. We're told a few cops will take the stand before the defense presents its case to the jury.

The "Sundress" hitmaker's former friend and alleged victim A$AP Relli took the stand last week and claimed his life -- personal and professional -- has crumbled ever since Rocky allegedly shot at him in Hollywood in 2021.