An A/C compressor is a special subset of a capacitor-start/capacitor-run induction motor. Relays have to be sized taking into account their particular characteristics.
The task is simple; take a look at your air conditioner's compressor plate, and look for a pair of values: FLA and LRA.
Which means Full Load Amps and Locked Rotor Amps.
Now, on the very first page of the datasheet you sent, look for the heading: contact ratings;
There are very many ratings depending on the nature of the load.
Look up for anything that says LRA/FLA. If your compressor's plate ratings are below the relay's ratings, then you are all set. If they are higher, then you will have to find a higher rated relay.
Otherwise, the operational life will be shortened considerably.