The Band Perry -- U.S. Skiers Crushed Our Song ... COME PLAY WITH US ON TOUR!!!

Country music superstars The Band Perry have invited members of the U.S. Olympic ski team to PLAY WITH THEM IN CONCERT ... after watching the athletes cover their biggest hit in Sochi, TMZ Sports has learned.

We know ... the band recently saw the incredible clip of Stacey Cook, Jacqueline Wiles and Laurenne Ross rockin' out to their huge song, "Better Dig Two" and LOVED IT!!!

In fact, a rep for the band tells us ... they've already been in contact with the Olympians in the hopes they can bring them on stage at one of their shows to play the song together.

The band even gave us this note to pass on to the skiers -- "We love you guys! Go Team USA!"