Yes you can, but IMHO it's way too tight. You will need everything to work (on the CX side) like clockwork, and maybe pray that the inbound AirAsia aircraft is running late.

Assuming on-time touchdown at 8PM sharp, another 10 minutes to taxi to gate, five minutes running (very fast) to Passport Control, 10 more minutes to collect your luggage, it will be 8:25PM. Your flight leaves at 9:20PM, which is 55 minutes before flight time. According to the AirAsia terms of carriage, they can deny boarding if the pax attempts to check in less than 45 minutes before flight time. The only safe assumption is that they will close the counter at 8:35. Remember there's no interlining therefore if you have check in bags with CX, you'll have to retrieve them, go through customs and proceed to the Air Asia check in counter on the ground side.

The good news aspects for you is that if you are traveling light (light hand carry only, so no check in baggage with CX), you can go direct to the AirAsia gate upon arrival in SIN without going through passport control provided you have printed out your AirAsia boarding pass in advance - then timewise you should be ok, Air Asia and CX both operate out of SIN terminal 1.