Aaron Rodgers and Danica Patrick's First Public Photo Together Fuels Dating Rumors

Aaron Rodgers and Danica Patrick seem to be rounding out the first lap of their rumored romance -- 'cause now they're dining together out in the open ... as seen here.

The Packers QB and NASCAR driver were spotted grabbing a bite Saturday night at The Mission Mexican restaurant in Scottsdale, Arizona, accompanied by a small group of people.

Eyewitnesses tell TMZ Aaron and Danica sat next to each other, but didn't show off any kind of PDA while there. We're also told other patrons recognized them, but left them alone.

Rumors have been swirling about the reported couple, who apparently got together shortly after the holidays. Word around town is ... things are moving fast with Aaron after Danica split from her BF of 5 years, Ricky Stenhouse Jr., late last year.

Looks like they have plenty of time on their hands to cozy up -- Aaron's season is over after the Packers didn't make the playoffs, and Danica's set to retire soon. Kismet!