The regiment was an organic element of the 28th Infantry Division. The 28th was originally a component of the Pennsylvania National Guard. Since he joined the division subsequent to its being called into Federal Service (17 February 1941), the Pennsylvania Adjutant General will probably have no record of his service. It's pretty late in the game but you might contact the division veterans association. The most current address I have is:
28th Infantry Division Association 329 Mansion Drive Alexandria, Virginia 22302-2904
You can inquire as to whether there is a 112th Regimental veterans association (and whether it's still active). Being private concerns, veterans organizations can usually only provide information on members, former members and other individuals who have had some sort of contact or dealings with the association. These organizations are rapidly disbanding as their memberships decline so be prepared for possible disappointment.