To be completely safe, throw the arrow away.

Thus said, I have cracked/split the nock end of a few arrows and have cut them shorter with success. However, I very very very carefully inspected them after making the shortening cut to be sure that the crack did not extend further into the shaft.

If you neighbor truly 'robin-hooded' your arrow, then there is probably more damage than is easily observed. I have never tried to repair such an arrow.

Be Careful.