A theory for a plasma wave wiggler has been described which employs the plasma whistler wave for producing laser radiation in a free-electron laser (FEL). While electromagnetically pumped FELs have been proven to be an effective means generating short wavelengths, practical difficulties occur in the design of these wigglers. For this reason, it is found that a plasma wave wiggler can be employed in concept with an electromagnetic wave wiggler due to both higher tunability and holding the focus of pump wave and e-beam over a significant distance to achieve a suitable amplification. Plasma in the presence of static magnetic field supports a plasma whistler wave. The plasma wiggler period can be tuned by varying the plasma density and/or ambient magnetic field. Electron trajectories have been analyzed using single particle dynamics and regimes of orbital stability have been demonstrated. A polynomial dispersion relation for electromagnetic and space-charge waves has then been derived, analytically. Numerical studies of the dispersion relation reveal that the growth rates are sensitive functions of the cyclotron frequency. It has been shown that by increasing the axial magnetic field strength (or cyclotron frequency), the growth rate for groups I and III orbits increases, while a growth decrement has been obtained for groups II and IV orbits.