Abstract: There must be electromagnetic fields created during high-energy heavy-ion collisions. Although the electromagnetic field may become weak with the evolution of the quark-gluon plasma (QGP), compared to the energy scales of the strong interaction, they are potentially important to some electromagnetic probes. In this work, we propose the coupled effect of the weak magnetic field and the longitudinal dynamics of the background medium for the first time. We demonstrate that the induced photon spectrum can be highly azimuthally anisotropic when the quark-gluon plasma is in the presence of a weak external magnetic field. On the other hand, the weak magnetic photon emission from quark-gluon plasma only leads to a small correction to the photon production rate. After hydrodynamic evolution with a tilted fireball configuration, the experimentally measured direct photon elliptic flow is well reproduced. Meanwhile, the used time-averaged magnetic field in the hydrodynamic stage is found no larger than a few percent of the pion mass square.