DCT: An act is right if and only if it is not prohibited by God.

Arguments for DCT:
Argument 1: The Bible says so.
The Divine Command Theory is found in the bible (the bible uses the word 'good' and 'right' as interchangeable with 'what God desires'). What the bible says is true. Therefore, DCT is true.
Argument 2: Precedent with Other Natural Laws
All laws were created by God (e.g., the physical laws were). Therefore, moral laws were. But to say that moral laws were created by God is just another way of stating DCT (which says that the moral is whatever is in accord with God's rules).
Argument 3: Objective Morality Needs a Source.
There are objective moral truths only if they have a source, an authority that created them. In other words, we are obligated to do behave in certain ways only if some authority says we must behave in those ways (cf. legal obligation and governments). God is the only plausible source of our objective moral obligations. And to say that God is the source of our objective moral obligations is just another way of saying DCT, that an is right just in case it's not prohibited by God.

Socrates Question (about piety):
Do the gods love a pious thing because it is pious, or rather is a thing pious because the gods love it?

Socrates Question (about wrongness):
Does God prohibit an action because God sees that it is wrong, or is the action made wrong only because God prohibits it?

Socrates says the former.  Two reasons to agree with Socrates: (1) otherwise, morality would be arbitrary -- God would have no reason to prohibit some act.  But this is implausible, God prohibits rape for good reasons.  (2) otherwise, God's goodness is trivial.  If we just define the right and the good as whatever God does, then God isn't good in any interesting sense.  It's just a trivial consequence of how we defined these terms.

Pete gave an interesting argument for taking the latter option: if we take the former route, then we limit God's power.  God would no longer have the power to create the moral laws.  But God is omnipotent.  So he does have the power to create the moral laws.  (This argument is reminiscent of Argument 2 above.)

Plato's Euthyphro Argument Against Theological Approaches to Ethics

1. If DCT is a true criterion of moral rightness, then actions are right because God permits them.
2. It is not the case that actions are right because God permits them. (rather, he permits them because they are right)
3. Therefore, DCT is not a true criterion of moral rightness.

- Be sure you understand why the conclusion of this argument is as it is, and not "Therefore, DCT is not true."
- Notice that someone who doesn't even believe in God would still say this is a sound argument. But they would reject premise 2 for a reason different from the one stated in parentheses.  They would reject P2 because they think that God doesn't even exist.  The idea behind Plato's argument is that, even granting that God exists and prohibits all and only the wrong actions, DCT still fails as a theory of moral rightness.