Which cut off frequency I should use in order to cancel AC noise with the low pass filter?
which cut-off frequency should I use?


Well if you are in the USA you would use 60 Hz and in other parts of the world it would be 50 Hz or 60 Hz but, that doesn't mean that the induced interference is at 50 or 60 Hz - it could be double this if it comes from the output of a bridge rectifier feeding (say) an amplifier. So, you need to establish what precisely the interfering frequency is.

Nobody here can tell you what that frequency is, only you can.


  I know I have to use a low pass filter


Normally this is done using a notch filter because it targets the specific frequency.

But, unfortunately it doesn't end here and it could be more complex than just filtering a single frequency. There could be harmonics (multiples of the AC or rectified AC frequency) and these can cause borader band interference.

Bottom-line: analyse what the problem is then work out where the noise source is then take remedial action with filters, shields, cancellation techniques and increased spacing/segregation.