How can I deal with Scouts as a Medic?

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:

• Try and hit the Scout with your Syringe Gun - if you can track them quickly enough. Don't have a Syringe Gun equipped? You're most likely out of luck, I believe one would encounter difficulty trying to hit a Scout with a Crusader's Crossbow.
• Pop your Übercharge and run - if you have an Über.
• Try and hit the Scout with whatever melee weapon you have - if they don't run out of your weapon's range before you hit them.

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:

• If you believe you have sufficient health...

  • You can try and hit the Scout with your Syringe Gun - Scouts have less health than other classes, and if you can track the Scout well enough, then you have a chance at killing them.
  • Note that while Scouts have less health than most classes, they can still pack a punch heavier and quicker than the others with their Scattergun.
  • Also note that you shouldn't try to fight a Scout with a melee weapon unless you have no other option, as most Scouts will be able to outrun you, shooting at you while they do.

• If you can't track the Scout well enough or you don't have too much health...

  • Pop your Übercharge. This is probably the better of these two options: in my experience, it's better to pop an Über early and survive than it is to wait, drop the Über, and die.
  • Rule of thumb: when in doubt, pop the Über.

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).

This related Arqade question comes to mind: the top answer of that question covers this question well (and probably better than I can), so I'll copy and paste it (with some added emphasis):

As the medic, your primary objective is to stay alive. If your ally is running somewhere stupid, don't follow him. Don't latch on to a single teammate and just keep him alive; keep everyone around you overhealed all the time.

If you are a good medic, your allies will protect you. If an enemy is coming straight for you, run towards an ally who can take him. Generally, as a medic, you should not be engaging in combat unless it is your last option.

If you keep your team healthy, they will have no problem keeping you alive too. Just stay out of the way.

I'm going to restate this point because it's extremely important: do not follow your teammates into certain death.

Medic can be a frustrating role because they can't do anything without competent teammates, but every team needs one.

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:

If you are with a large group, you don't need to be up at the front line.

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).