This joist can be repaired using a joist repair plate. These are made from structural steel and they have holes in them so you can lag bolt them into the framing member to reinforce it.
I haven't been able to find a good image of one, but it will be similar to this.
The one pictured is not properly sized for your needs, and the construction doesn't appear to be heavy enough either, but you will get the idea. You most likely would have to have one custom fabricated.
To install it, you would need to jack the joist back in place and place temporary supports on both sides of the area to be repaired. Then slide the plate into place and attach it with bolts.
This crack doesn't appear to be very serious, so you could probably fix it on your own. If you see more signs of failing joists, you should consult an engineer to assess the issue.