I am recovering from a broken elbow. Is swimming a safe way to build muscle and get in shape?

Yes. Assuming that the fracture is completely healed and you have been told to start exercising, swimming is an excellent way to rehabilitate and strengthen muscles that have been immobilized due to a fracture. Consult with your physician or physical therapist on which specific aquatic exercises can be beneficial for your particular condition.
Yes. As long as your doctor has said the bone has healed, swimming is great.

Related Questions

I am recovering from a broken elbow. Is swimming a safe way to build back muscle?

Yes. As long as the bone healing is sufficiently advance to withstand the demands that is based on exam and xray findings, although xray frequently lags the clinical healing.