Spintronics materials have recently been considered for radio-frequency devices such as oscillators by exploiting the transfer of spin angular momentum between a spin-polarized electrical current and the magnetic nanostructure it passes through. While previous spin-transfer oscillators (STOs) were based on in-plane magnetized structures, here we present the realization of an STO that contains a perpendicular spin current polarizer combined with an in-plane magnetized free layer. This device is characterized by high-frequency oscillations of the free-layer magnetization, consistent with out-of-plane steady-state precessions induced at the threshold current by a spin-transfer torque from perpendicularly polarized electrons. The results are summarized in static and dynamic current-field state diagrams and will be of importance for the design of STOs with enhanced output signals.