What will happen if we use an Inductor in place of a Capacitor in Single phase Induction motor
The whole point about a coil that is series fed with a capacitor is that at the right frequency it will naturally produce a phase shift of 90 degrees and this creates a pseudo-rotating magnetic field that is good enough to start rotation in the correct direction. Consider this RLC circuit and response below: -



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If the coil has an inductance of (say) of 100 mH and the capacitor is 100 uF (just as a thrown together example) then, at 50 Hz it will produce a phase angle for the coil voltage that is 90 degrees shifted from the main applied voltage.

If the coil inductance was 1 henry and the capacitor was 10 uF it would produce the same angle. 

Single phase induction motor with start and run capacitor: -



The above diagram shows a single phase motor with a start capacitor and a run capacitor. Usually the start capacitor is bigger in value than the run capacitor and naturally tunes to a lower frequency hence produces a better starting torque. When the motor is up to (say) half-speed the centrifugal switch will open leaving just the run capacitor that is more "tuned" to running the motor at full speed.

Clearly there are some motors with only a run capacitor and some motors with only a start capacitor and this depends on application and power.


  So i was wondering what will happen if we use a an inductor, i mean
  doesn't it create phase shift like capacitor and make rotating field ?


An external inductor replacing the capacitor won't change the phase angle of current in the start/run coil - it will be the same phase (or thereabouts) as the current in the main coil and there will be no rotation of field.