Tank anxiety isn't a thing. Being nervous about tanking is a thing, as-is being nervous about doing anything new or different in life. I was nervous about getting a dog, I felt a little anxious about it. I did not have an anxiety disorder over it.
Calling anything that you're nervous about an anxiety does a disservice to people who actually, genuinely, have anxiety disorder. Which is categorized as a state of excessive uneasiness and apprehension that generally results in panic attacks or disruptive behavior, enough so to disrupt a person's way of life.
I really wish people here would stop dropping the A-word for big ol upvotes because every time you do, it makes someone somewhere roll their eyes and go "Anxiety isn't a real thing". But every dingdong goddamn day we got another thread or three about "my anxiety!" over playing a tank in a video game or joining a freakin' dungeon or farming up a damn mount in a group where no one speaks anyway.
Be afraid of fucking up, be worried that you might screw up and kill the whole group. You're nervous about that and that's OK, but there is no magic cure-all for it; Just tank and get used to it. Watch some videos, learn how to play your class. Your first group or two might suck, it'll feel like shit when you get in a group with some asshole that's pulling everything for you and aggravating you - But those people are rare. They exist, accept it and move on.
I was in an expert roulette group last night, the literal last dungeon in the game, tank was a warrior that almost never used tank stance, didn't know what to do for any of the bosses (or didn't care, who knows), pulled 1 group at a time. No one cussed at him or even really gave a shit, I put up youtube videos on my other screen and just zoned out during trash. Tank fucked up damn near every boss mechanic on the first two bosses and still didn't die.
Fact is you can be a colossal fuckup and still be alright. Get out there and try it out. Sorry if I sound like a dickhead, but y'all are crying wolf often enough in here that eventually anxiety is going to be thought of in the same terms as gluten intolerance.