Is there a relay to increase rpm when AC kicks on in a 2011 Ford escape IL 4? If so how to replace?

No. The computer has total control of the Throttle Body in your Fly-by-wire system. Why do you ask?

Runs fine until the AC kicks in then occasionally runs rough almost to the point of stall. Any ideas on the cause and a cure?

A couple of suggestions: First the basics - check condition of the Motor Mounts, vacuum lines (especially the tubing from the air cleaner to the throttle body), and PCV. Ford has a TSB out #11-3-22 that addresses intermittent concerns without Check Engine Light or codes present - ISSUE Some 2009-2011 Escape, Mariner, 2010-2011 Fusion and Milan vehicles equipped with a 2.5L or 3.OL engine built on or before 03/04/2011 may experience a leaking/stuck canister purge valve. This condition may cause various intermittent driveability symptoms without any diagnostic trouble codes (DTC). The condition may also cause driveability symptoms with malfunction indicator light on with DTCs P144A, P2196, P2198, P1450, or P0456. 1. Remove evaporative emission canister, refer to Workshop Manual (WSM), Section 303-13. 2. Inspect canister for raw fuel by turning canister over and watching for any signs of raw fuel exiting canister. Are there any signs of raw fuel present in the evaporative emission canister? a. No - Proceed to Step 3. b. Yes - Replace the evaporative emission canister, Refer to WSM, Section 303-13. Proceed to step 3. 3. Replace the evaporative emission canister purge valve located in the engine compartment, If your vehicle is low mileage it may be under emissions warranty

Thank-you I'm not a mechanic ,some direction on how to check for vacuum leaks would help along with where to find the workshop manual you refer to .

Your local parts store will have a manual that can help you locate and check that canister (O'reilly, Autozone, etc.) As for checking for those leaks, look for anything that might be disconnected, loose clamps or have a "hiss" sound while it's running.

Check the throttle plate to see if it's got dirt or oil that may cause it to stick.. also the throttle body in those cars are known to be faulty... ford may have extended coverage on it also

While Emissions Warranty will cover a faulty Throttle Body, a sticking Throttle plate will kick a code on this particular fly-by-wire system. If the input requested by the pedal and demanded by the PCM doesn't match the exact position of the Throttle Plates, the vehicle will go into a "Fail Safe" Mode in which the Check Engine Light will come on, the Throttle response and available power from the engine will be greatly reduced. Since there is no actual cable connected to the Throttle plates - there can be no room for error.