Ezekiel Elliott Babysits Rae Sremmurd's Chick Magnet Dog

Ezekiel Elliott had the ultimate pickup line at the Rae Sremmurd show Thursday night -- Swae Lee's ADORABLE puppy ... and the chicks looooved it!

The Dallas Cowboys superstar is tight with the rap group -- in fact, they even brought Zeke onstage during their concert in Dallas.

They also tasked him with the ultimate responsibility of watching Swae's beloved pooch, Boom, during the show ... and he accepted.