Flexible interference patterning is an important tool for adaptable measurement precisions. We report on experimental results of controllable two-photon interference fringes with thermal light in an incoherent rotational shearing interferometer. The two incoherent beams in the interferometer are orthogonally polarized, and their wavefront distributions differ only in an angle of rotation. The spacings and directions of the two-photon interference fringes vary with the rotation angle, as illustrated in three cases of two-photon correlation measurements in experiment.