We demonstrate a method to create arbitrary terahertz (THz) polarization profiles by exploiting the magnetic field dependent emission process of a spintronic source. As a proof-of-concept, we show that by applying a specific magnetic field pattern to the source that it is possible to generate a quadrupole-like THz polarization profile. Experimental measurements of the electric field at the focus of the THz beam revealed a polarity flip in the transverse profile of the quadrupole-like mode with a resulting strong, on-axis longitudinal component of 17.7 kVcm-1. This represents an order of magnitude increase in the longitudinal component for the quadrupole-like profile compared to a linear polarization, showing an example of how magnetic field patterning of a spintronic source can be exploited to obtain desirable THz polarization properties. This unique ability to generate any desired THz polarization profile opens up possibilities for schemes such as rotatable polarization spectroscopy and for efficient mode coupling in various waveguide designs. Furthermore, the strong longitudinal fields that can be generated have applications in areas including intrasubband spectroscopy of semiconductors, non-diffraction limited THz imaging and particle-beam acceleration.