As a Medic, I find that Scouts are very hard to kill, as they spin around in circles and shoot me while I'm spinning around trying to keep up with them. How do I deal with them?
As a Medic, you don't have too much of a defense against any class, much less a Scout, by yourself. If confronted by yourself, you have maybe three options:
By yourself, you have no real viable options, especially when a Scout with proficient aim can two-shot you with a Scattergun faster than you can track and pin them down with a Syringe Gun.
The only real weapon you have is your teammates: therefore, you should never fight an enemy by yourself unless you have no other option - instead, help your teammates fight the enemy by healing them.
If you ever find yourself alone and confronted by a Scout, only two of the above options are viable:
Whichever option you choose, as @badp mentions in this question's comments: it would be wise to also call for help (the default keybind is C+1).
The second answer to the question is also very informative. I won't copy and paste all of it here, just this one excerpt that is worth mentioning:
In summary: the only real weapon you have against Scouts (and the majority of the other classes) are your teammates. Don't venture too far from your teammates, because if they're any good, they will protect you (and you, as a good Medic, will protect them by healing them).