Yes. On the Planetary Details screen, there is a "Set as Homeworld" button that places the capital on that planet.

Oh, those capitals.

As far as I know there is no way to decommission them, making it even more important where you place them, and furthering the mystery of why the AI always seems to build them all on their homeworld.

They're really good things to capture, because although you can only build one, you may own and use as many as you can get.

There's some more fine print you'll want to know about, too: Civilization Capitols.

If you conquer an enemy civ's homeworld they just move their capitol somewhere else.  If their last planet is a barren Class 3 rock, congratulations, you just wasted a very rare and valuable building by maneuvering it there.

What you want to do is leave the choicest, best real estate for last, so when you conquer the Civ Capitol it'll be someplace you can actually make use of it.

Check out the 20% morale.  That's the equivalent of 4 Entertainment buildings as opposed to the standard colony's 5%.  There are other extras as well, but for me the 20% morale is the real boon.  You don't want that stranded on the dark side of the moon.

Which is why I always make building my capitals a priority as soon as I research the respective tech.

Also, I don't think you gain control of a race's Civilization Capital even if you capture all their planets - I'm pretty sure that it just becomes an "initial colony" structure instead.

The mystery is why the AI always moves it to their 'secondary' planet if you take their homeworld. For example, if you take Earth, the capital always first moves to Mars. As you said, it's not something you want on a Class 3 rock, so it's an open question why the AI does.