The epoch International Celestial Reference Frame (epoch ICRF) is proposed as a new concept in order to consider the effect of apparent proper motion of the position of a radio source due to acceleration of the spatial origin of the ICRF, the centre of mass of the Solar system. This apparent proper motion has a magnitude of approximately 5.8-microarcsec ({mu}as) per year, and for the 30-year very long baseline interferometry (VLBI) observational history these position variations will exceed 100{mu}as. We show that the dipole structure of the apparent proper motions leads to global rotation in the ICRF2 and the main term, the shift of direction of the origin of right ascension, reaches 25{mu}as per century. The 'epoch ICRF' is constructed using epoch positions at J2000.0 and apparent proper motions of radio sources, which are reported here for 295 ICRF2-defining sources.