A folding chair frame structure includes left and right supporting frame units, front and rear connecting frame units, and a pair of armrest supporting rods. A top of each armrest supporting rod has a spherical head. Each armrest supporting rod has an engaging groove below the spherical head. A pair of armrest rods is pivotally connected to respective rear parts of the left and right supporting frame units. A front end of each armrest rod has a joint. A lower end of the joint has an accommodating chamber. A side wall of the accommodating chamber has at least one receiving opening. An engaging plate is detachably inserted in the receiving opening. The engaging plate has a through hole. When the spherical head is inserted in the accommodating chamber and passes through the through hole, the engaging plate is engaged with the engaging groove.