No, you can't repair CF, but you might be able to salvage the part. Once the resin on CF has cracked, that's it. There are ways to salvage CF parts, but the only way they will be as strong as the original is if they have re-enforcement added, more weight.
The crack you describe might go right through the part and the only thing holding it together is the fibres. In this case, you can glue or bolt some plates to either side to take the load. If the cracks are surface only, you could fill the crack with super-glue, clamp it in a vice to close the cracks up and hope that it holds together.
My experience is that once it is cracked it is weak and whatever you do it will eventually fail. However, if you glue or bolt a couple of plates to each side that will transfer the loads away from the cracks, the part will last much longer. HTH
