Rihanna and A$AP Rocky went celebrating Thursday night … toasting to RiRi on her 37th birthday — and, Rocky’s even got jokes about new music.

The Hollywood power couple hit up the Nice Guy in L.A. — a cozy Italian joint with an old-school feel — and, they were absolutely mobbed by photogs outside … dozens of cameras flashing as they left the place.

Rihanna shields her eyes from the cameras, but doesn’t say much as she’s heading to the car … while Rocky asks people to move so he can walk around to the other door.

Later on, another man brings out what looks like food art … a stack of pancakes and what looks like a bowl of cereal with a big milk splash holding up a spoon.

Unclear if this is the cake for RiRi’s birthday … but, it’s certainly an impressive piece of craftsmanship.

It’s a week full of celebrations for the happy couple … ’cause not only did Rihanna turn 37 on Thursday, but A$AP Rocky was acquitted of two counts of assault with a semiautomatic weapon, which could’ve landed him in jail for nearly 25 years if he was convicted.

While at least one juror has said she thought the gun in the case was real and not a prop gun, she said she didn’t think there was enough evidence to convict … but Rocky’s lawyer Joe Tacopina told us he was sweating out the verdict.