Nikki Glaser Cracks Joke About Scottie Scheffler's Arrest at ESPY Awards

Nikki Glaser came out swinging at the ESPY Awards ... cracking a ton of jokes at several athletes' expense -- and Scottie Scheffler's legal troubles were not off-limits.

The comedian brought out the big guns at the Dolby Theater in Los Angeles while presenting the award for Best Male Athlete to "peak athletes who push their bodies to the limit and also a golfer."

She then apologizes to the golfer in question -- Scottie Scheffler -- saying she knows it's difficult to putt, chip and drive ... over a cop's leg.

As you know ... SS was facing one felony count in addition to three other misdemeanors, after he allegedly dragged a cop with his vehicle outside of the PGA Championship in Louisville back in May.

Scheffler said he didn't mean to blow past the guy, adding the whole situation would've gone differently if he'd known he was speaking to a cop in body cam footage from the incident.

Jefferson County prosecutors filed to dismiss the charges a couple weeks after the incident ... chalking up the incident to one big misunderstanding.

BTW ... Scheffler wasn't the only athlete Glaser took aim at -- she also cracked jokes about Tom Brady, the NFL's obsession with Taylor Swift and Patrick Mahomes. Check out the clip to hear all her best one-liners.