You will be able to get a Compass Card at the airport, either before or after you claim your baggage.
From the MTS web site:
Ticket Vending Machines for MTS services are located near the Information Centers of both Terminals 1 and 2, as well as at the Middletown and Santa Fe Depot stations. Ticket Vending Machines sell Compass Cards with one day passes, multiple-day passes, and monthly passes. You may also reload your existing Compass Card. The machines accept cash (and give change up to $15) and credit cards.