How can I install an electric dryer using the old air conditioning circuit in my breaker box
In answer to you question - It is not possible to use any circuit in the panel you are showing unless you want completely replace the AC circuit. I am assuming the 20A 2 pole circuit in the lower right is your AC circuit. Regardless, all of the circuits shown are 20A.

NEC Article 220.14 (B) and (C) prevent you from using a 20A circuit for a dryer load. 220.14 (B) refers you to 220.54 which states all dryer circuits need to be rated for 5000VA, that would be 20.9A at 240V. 220.14 (C) refers you to motor loads which state you have to add 25% for motor start up. So a minimum circuit size for a dryer would be 30A 2 pole with #10 wire conductors.

Hope this helps.