What's the reason for the poll
You might as well have asked "Can I get a flight to the moon" The logical answer is "yes" but reality is a totally different matter. You may well get lots of "Yes" and "No" answers but will be no better informed whichever way the poll falls
If you want the answer to a perfectly valid technical question then your simple question suffices.
Single phase (squirrel cage type) AC motors may be considered analogous to a slipping mechanical clutch. You can control speed by varying the supply voltage but the speed becomes very dependant upon load. In short, it can be done but neither reliable nor recommended. If however the motor is a universal type, with commutator and brushes then speed control is easily achieved since the motor may be considered as "DC" unit and varying voltage will vary speed. Such devices were once universally available for the likes of drill control.
If you really want to control speed of an AC motor the best way is to use a 3-phase motor with a variable frequency inverter drive powered from the single phase supply. Some of these accept low level analogue DC control signals which your Arduino PWM can produce once you've filtered it to produce a 0-5 volt analogue signal.