Aaron Rodgers & Danica Patrick: First Coupley Public Event

Aaron Rodgers and Danica Patrick took a big step on Tuesday ... going out to their first big celebrity event as a couple -- and TMZ Sports has the pic.

Aaronica (yeah, we did that) hit up the AT&T Pebble Beach Pro Am on California's Central Coast -- where Aaron is competing in the golf tourney. FYI, dude's a stud golfer.

The couple went public with their relationship last month after they were spotted at a private dinner date in Arizona with friends.

Gotta admit ... they look damn good together.