Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Less Severe; Inflight Event / Encounter Bird / Animal
Aircraft Aircraft Damaged; Flight Crew Landed As Precaution; Flight Crew Returned To Departure Airport
Aircraft
Just after taking of runway 09R in ZZZ we were climbing out of approx. 10;500 feet when I saw something black and of roundish shape out of the corner of my eye from left to right.  It impacted the aircraft.  My First Officer (FO) stated 'that's a bird'.  As soon as it impacted the aircraft we immediately got an ECAM for ENG 2 STALL.  Assuming that it was a bird we felt that it had gone through the engine.  My FO stated that he also saw the engine indications decrease.  We requested ATC to level of at 13;000 feet and to turn back to ZZZ.  The engine did stabilize and seemed to be working normally.  The FO briefed the flight attendants and then I made an announcement to the passengers.  A normal approach and landing was made.   We were below max landing weight.  We pulled off of the runway and had the emergency crew do a drive around the aircraft as a precaution.  They stated that they did not see anything unusual so we taxied to the gate normally.
An A319 Captain reported abnormal engine indications after a bird strike shortly following takeoff. The flight crew elected to return to the departure airport.