We propose to generate terahertz surface plasmon polaritons (SPPs) on a metal wire by launching electron bunches onto a tapered end of the wire. To show the potential of this method, we solve Maxwell's equations for the appropriate boundary conditions. The metal wire tip is modeled by a perfectly conducting semi-infinite cone. It is shown that the SPPs can be recovered from the idealized fields by well-known perturbation techniques. The emitted radiation is strongly concentrated into a narrow solid angle near the cone boundary for cones with a small opening angle. We calculate that, using currently available technology, subpicosecond SPPs with peak electric fields of the order of MV/cm on a 1 mm diameter wire can be obtained.