I am replacing a dryer that had a 3 prong plug with one that came with a 4, can I rewire for a 3 prong as that is what the house is wired for

You need to check the electrical instructions that came with the dryer.

If the instructions allow a three wire connection that just follow the instructions. If the dryer requires a four wire connection, then you have to replace the cable and receptacle to a four wire configuration.

The device electrical instructions govern the connection.

Dryer installation manual will have both a 3 wire and a 4 wire connection diagram. 4 wire adds an extra ground to the cabinet whereas the 3 wire used the neutral as a ground. Do not put a 4 wire receptacle in and only connect a 3 wire cable to it.

The dryer will not require a 4-wire connection.
If your house has a 3-wire receptacle you just replace the existing cord with the proper 3-wire cord.
This is literally what you need to know:
Attachment 47836
Some dryers will have a green wire for the ground and not a strap. In this case the green wire goes under the same screw as the white, or center conductor, of the cord.