Electrical control of magnetism of a ferromagnetic semiconductor offers exciting prospects for future spintronic devices for processing and storing information. Here, we report observation of electrically modulated magnetic phase transition and magnetic anisotropy in thin crystal of Cr$_2$Ge$_2$Te$_6$ (CGT), a layered ferromagnetic semiconductor. We show that heavily electron-doped ($sim$ $10^{14}$ cm$^{-2}$) CGT in an electric double-layer transistor device is found to exhibit hysteresis in magnetoresistance (MR), a clear signature of ferromagnetism, at temperatures up to above 200 K, which is significantly higher than the known Curie temperature of 61 K for an undoped material. Additionally, angle-dependent MR measurements reveal that the magnetic easy axis of this new ground state lies within the layer plane in stark contrast to the case of undoped CGT, whose easy axis points in the out-of-plane direction. We propose that significant doping promotes double-exchange mechanism mediated by free carriers, prevailing over the superexchange mechanism in the insulating state. Our findings highlight that electrostatic gating of this class of materials allows not only charge flow switching but also magnetic phase switching, evidencing their potential for spintronics applications.