yes, use a soul gem on it, or alternately head to a mages guild - you can pay some members to recharge them. For the soul gem method, the gem itself needs a soul trapped in it. To do that, use a 'soul trap' spell on something (non humanoid) before you kill it, and when it dies (assuming the trap effect is still active) its soul will be captured in the smallest soul gem that will accomodate it. Different levels of souls contain different amounts of energy to charge the weapon with. Using a soul gem will consume it.
You can also use soul gems in the arcane university (when you've gained access to it by joining the mages guild) to enchant existing weapons with a variety of spells.. Again, more powerful effects can be achieved with greater levels of soul.
There are also a few other things about them worth mentioning, but worthy of spoiler tags:
The enchanting/soul gem system is rather dumbed down from Morrowind, where you could apply any spell effect you knew to any item you had, restricted by your enchanting skill, the type of soul, and the item you were enchanting. Same thing for spellmaking. You could choose any spell type, any target, magnitude, range.. even constant effects. Much more interesting system, that fit well with the 'openness' of the game.
It's kinda a pity they ditched it for Oblivion.