Beowulf must battle Grendel with his bare hands because

Because he sees it as the honorable thing to do.

The sense of honor Beowulf displays here is one of the main themes of the poem. Beowulf sees using a weapon against a beast that uses no weapon as dishonorable. He will fight Grendel on equal terms. Grendel is charmed and cannot be cut by swords, but Beowulf does not know this as far as a reader can tell, and this is not why, according to his own words, he refuses to use a sword.

As he says:

... I have heard,

Too, that the monster's scorn of men

Is so great that he needs no weapons and fears none.

Nor will I. My lord Higlac

Might think less of me if I let my sword

Go where my feet were afraid to, if I hid

Behind some broad linden shield: my hands

Alone shall fight for me, struggle for life

Against the monster. God must decide

Who will be given to death's cold grip. (261-270)