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
Your power steering pump and or steering box may be about to give out on you.
Engine miss.
What make the steering wheel shake is the tires that need wheel balance.
During acceleration? I'm not sure. But when both idling and acceleration the engine's combustion can cause a lot of vibration in the steering wheel if you are in an older vehicle.
Not the steering wheel shake itself, however what is causing the steering wheel shake, can certainly be extremely dangerous and potentially cause you to lose control of the vehicle. **GET IT CHECKED OUT BEFORE THAT HAPPENS**
check your powerstearing pump for fulid or belt slipping , most commond cause. hope this helps dave
sitting and idling ?possible bad engine or trans mounthave them inspected
Wheel balance
Motor is idling rough.
Yes A VERY common concern is steering wheel shake due to ice in the rims
Yes, it is possible. Any loose/worn front end part can cause steering wheel to shake.
usually your cars out of alinment