I dunno about getting anxious whilst revising(!) because I never had that problem so much, just a vague sense of stress, but for feeling anxious in OSCEs I do have some advice. One obvious one is to prepare as much as possible! I mean you'll feel anxious anyway even if you prepare to the max, but it's easier to feel more confident and less anxious if you actually have grounds to feel confident :P Practising with others is always good because you also get a feel for how you perform compared to other people and it means you're exposed to a less textbook situation - it's always good in an OSCE group to try and push each other, like have the actor try to be a poor communicator etc., or ask tangential questions because you'll all learn that way and get used to being adaptable in stations.
Second make the most of your prep time before each new OSCE station. It's absolutely golden and you've got to do two main things in your 30 seconds or whatever it is:
1. Actively clear your mind of the previous station - like tell yourself directly "forget it". Way too often you'll find yourself still panicking or thinking about the last station and this drags over onto the next one, and you often won't realise you're doing it until the beep goes off or you've already flustered yourself for the next one. So move onto the next station and mentally make an effort to just re-set yourself and be objective again, no matter how badly or well the last station went.
2. Figure out what you think the marks are going to be for. Once you've figured out what they want from you, you'll not only stand more chance of gaining exam points but you can also relapse into a kind-of structure which helps you perform in the station and feel like you know what you are doing... which will make you feel less anxious! I used to try and imagine what the mark sheet would look like. I mean you'll have seen plenty of mark sheets in your revision time to guess at this.
You'll never not feel anxious in OSCEs, I don't think it's human to - it's more about managing your fear I would say haha. Realise when it's damaging you, snap out of it and have an unemotional practical way to approach each station. Even if you read the blurb and realise you don't really know what it's about or the topic or whatever, you still know that you can score points on the mark sheet just by doing the basics.
I used to tell myself that I needed to relax and just give myself my own best chance or I really WILL fail, and that usually helped me focus/calm down a bit, especially after I felt like I'd bombed something.
Good luck! And also - you've not failed until you have failed :P It's hard but distract yourself and try to pretend it's not happening until results!!