Can you run a three phase motor at your house?
Not with standard residential electricity. Homes are normally wired for single phase power. There are electronic invertor devices you can buy to run a small 3 phase motor on single phase but the costs are quite high.
If the equipment you need the motor for has the option of using a single phase motor - or can be adapted to take one at reasonable cost - it is often better and cheaper to part-exchange an unwanted 3 phase motor for a suitable single phase motor.
If you decide you really need to have 3 phase in your home, your electric power utility company may be able to install a 3 phase service but the costs of doing it will depend a lot on the distance that your home is from the nearest 3 phase substation...