What is the feasibility of converting an F-22 to carrier use?
In general, land based aircraft do not lend themselves well to carrier conversion. On the other hand, conversion in opposite direction is (relatively) easy, as shown by F-4 and F-18.

Conversion of aircraft to carrier use require a number of modifications:


Tail hook has to added and rear fuselage reinforced for arrested landings.
Landing gear has to be strengthened for high sink rate (~24 ft/s).
Atleast in USN, the front landing gear and fuselage has to be strengthened for catapult launches.  
Also, it requires additional equipment, like th Carrier Landing system, redesigned refueling system (pretty much everyone use a system different from USAF).
Carrier based aircraft usually are expected to have better low speed capabilities as they have to fly slower approaches and wave-off (go-around) at lower speed compared to the land based aircraft. This dictates the wing loading, resulting in increased wing area and/or high lift devices.
There are also issues in corrosion prevention etc.


The weight penalty due to these reasons can be non negligible. For example, the naval Rafale M version weighs nearly 500 kg more than the Air Force Rafale C variant (which has ~10 ton empty weight). USN calculated that the NATF (Naval Advanced Tactical Fighter) will be around 1800 kg heavier than the Air force version (ATF was supposed to weigh ~15 ton).

Another thing is that the USAF and USN had different requirements, for example, the USAF wanting a single seater and USN wanting a double seater, requirement of different sensors (for fleet defence) etc. in the end, the aircraft proposed for the NATF looked nothing similar to the one that finally became the F-22 and the project was quietly buried.



F-22 NATF proposal, image from aerospaceweb.org

Note that the design has swing wings, as the aircraft was being proposed for replacing F-14 Tomcat. Another important result of the navalization of the aircraft is the reduction in the number of planform alignments, and their negative impact on the stealth characteristics. 

Carrier conversion of F-22 could have been done if it was considered early in design. Doing it now (note that NATF was considered due to the insistence of Congress; it is doubtful if USN ever wanted it). Doing so later in the design process will result in another F-111B fiasco. As for doing it now, it is better to design a new aircraft (which was what the F-35 is).