I don't think so, a triac's gate is connected to the AC mains system which is not a safe concept with a Dc powered arduino. Also a triac needs to be switched in synchoronous with the AC mains.
Do you want to turn the AC motor On/Off or are you attempting to control its speed via variation of the supply voltage. Is the motor a squirrel cage type unit or a universal motor (with brushes).
More details required of exactly what it is you are trying to accomplish.