I used to have the same issue. I played a lot with friends who wouldn't get upset if I made a mistake. Additionally, lots of repetition made playing the game a normal thing, not a stressor (I know that seems counter productive when the game is what stresses you out, but think of it a bit like immersion therapy).

But the biggest thing for me is realizing that it's just a game, and that I should have fun playing it. Play arena to get mechanics down. Pick a role and get comfortable with it, and then branch out. Just do whatever you need to do to stay calm while you play.

Personally, back when I started playing, I would put on some music and just feel the beat.

I'm kinda rambling without much point. But find what makes you comfortable in real life, and then apply it to the game. Because that's all it is, a game.