Does Clash of Clans have a building that allows troops to defend your base?

If you are in a clan, and other members of your clan donate troops to you, they will be stored in your clan castle and come out for defense. This is the only way that I know of to defend with troops. So no, you can't train troops and use them for defense. However, others may donate troops that you can use for defense. Also, skeleton traps may be considered troops by some, even though they are not trained.

There is no way to self donate.

You can store your own troops in your clan castle if you have multiple accounts and donate to yourself from your other account(s).

By the way, one good reason to join a clan is that clans with higher experience (Experience level 5 and up) can donate stronger troops - and so can you. For example if you are in my clan and I give you my Level 5 giant, it becomes an Level 6 giant for you. Using this clan perk my TH9 account can give my TH7 account max Giants (Level 7) and max Dragons (Level 5).

The Clan Perks are described in SuperCell's documentation and even in the game.