you need an arrangment of two mirrors to flip the rotation. for example, if vertically (z-direction) polarized light is traveling in x-direction you can put a first mirror to reflect the beam towards the z-direction (the polarization is now in x-direction). when you put a second mirror that reflects the beam towards the y-direction, the polarization will be horizontal.

ps: with a third mirror you can direct the beam into the original x-direction maintaining the horizontal polarization

I can suggest similar to Jonatan arrangment made of 4 TIR prism for Your task. See attached file 

If you change linear polarization to circular using a quarter wave plate (QWP), the polarization of the reflected light would also be circular but with reversed direction. If the reflected light passes through the QWP once more you obtain perpendicular polarization. This is used in optical isolators that block reflections using a linear polarizer and a QWP.

Just to add to what has already been said, there is such a thing as a reflective wave plate based on the relative phase shift between the s- and p-polarized components incident on a metallic surface. The physics behind this approach is similar to that of the TIR prisms, except it doesn't require propagation through bulk material (not possible for high-power or short-pulse/broadband light sources). The only commercial product that I'm currently aware of can be found in the link below. (It's quarter-wave rather than half-wave (like you specified in your question), but perhaps it could still be useful to you.)

http://www.femtolasers.com/fileadmin/documents/Leaflets/FEMTOOPTICS.pdf#page=99