Abstract: Let k be a field. Totaro studied the de Rham cohomology of algebraic stacks over k, and computed it for classifying stacks of linear algebraic k-groups in many cases. Combining previous work of Drury, May and Epstein, I define and study Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field k of characteristic p>0. These operations share many properties with their topological analogues, but there are also important differences. I then determine the Steenrod operations on the de Rham cohomology of linear algebraic k-groups computed by Totaro.