Your doctor has some alternatives to surgery when treating ankle fractures. One is to stabilize the ankle without manipulating the broken bones. A cast, splint, or bandage may be used to hold the bones in place until they heal. This can be done for a fracture in which none of the bones have moved out of place.
The second is to manipulate the ankle from the outside of your skin, to move the broken bones back into place, and then apply a cast. This is called a closed reduction.
The choice of treatment that your doctor recommends depends on the type, location and seriousness of the fracture. Therefore, depending on your specific fracture, the alternatives just mentioned may or may not be appropriate for your situation.
However, if you are uncomfortable with the option of surgery, you should discuss this with your doctor.