We report upper limits to rotation from the measurement of line breadths via cross-correlation analysis for 27 RR Lyrae variables. The eight best-observed stars of type RRab show the same variation of breadth with phase: the breadth peaks sharply during the rise to maximum light, drops gradually, and reaches a broad minimum during the phase of maximum radius. During this phase the breadth is always narrow, consistent with instrumental resolution and turbulence alone. For the three well-observed RRc variables, the breadth is this narrow at all phases except for a slight increase during the rise to maximum light. The remaining stars also conform to these patterns, albeit with sparse phase coverage and lower signal-to-noise ratio. We interpret these results as indicating that lines are broadened in RRab stars by shock-induced plumes or turbulence during the rise to maximum light, and perhaps by other causes as well, but not by rotation in RR Lyrae stars of either type. We estimate an upper limit of v sin i < 10 km s-1 in all cases. This is in stark contrast to the rotation seen in field blue horizontal branch stars, where v sin i > 10 km s-1 in three out of six well-studied field stars, and to the more rapid rotation, often exceeding 100 km s-1, of the Population I delta Scuti variables which occupy adjacent regions of the instability strip.