Why does your steering wheel shake when engine is idling?

Sounds to me like a motor mount may have lost it's rubber barrier or the motor mount broke all together , how ever if someone put headers on the car and they touch the rack even slightly you will feel every vibration from the motor, depending on the make of car it should be a simple fix, Again depending on the make of car some front wheel drive cars have transmission linkage that When placed in park the linkage may hit the rack & pinion a close visual look of the rack & pinion under the hood might reveal the culprit just visually follow "from the steering wheel you should see a rod that runs to it this is mostly called a steering column.

My guess would a a bad motor mount and the motor is listing on one side resting the exhaust on the column, Or it could be a bad harmonic balancer but the entire car would shake if that was the issue . What kind of a car is it .1990's.Mustang by chance?

My Guess

The engine has a "miss" at idle and requires a diagnoses and repair