How switch 20A AC between 2 wires
SOME FETS around that size are usable.
You will need two in series with opposed polarity for AC.
Join Gates.
Join Sources.
Two Drains are an AC switch terminals.
Drive gate to source with floating voltage (details if needed). 

BUT with say 5 milliOhm FETS your dissipation is
I^2 x R = 20 x 20 x 5/1000 = 2 Watts per FET.   

With 1 milliOhm FETS that's 0.4 Watts/ FET. 1 mO FET is "special but doable".
Careful design and heatsinking needed.
What are your size constraints and why?

Slightly larger. Just.
5mm x 6mm x 1mm.
30V 100A+.
Under 1 milliOhm so eg say ~ 0.5W at 20A.
In stock Digikey $1.98/1
http://www.digikey.com/product-detail/en/PSMN0R9-30YLDX/568-11554-1-ND/4965575

Datasheet here  

Heatsink well enough and they will work well.
Need not be "large" but must be adequate.   

Larger version ofdiagram here





Added:

I just found this earlier SA Q&amp;A  

What transistor or combination of transistors should I use to make a fully controllable AC switch?

Diagram below from Andy's answer matches what I described above.
Isolated gate drive need not actually be truly isolated - ask.