The ability to efficiently transmit and manipulate high-frequency signals poses major challenges resulting in a lack of active and reconfigurable millimeter-wave and terahertz devices that are needed to enable beyond-5G broadband communication systems. Here, thin single-walled carbon nanotube (SWCNT) layers are introduced as a tunable impedance surface for millimeter-waves. Carbon nanotube layers are integrated with dielectric rod waveguides. Their surface impedance, tuned by light, is shown to modify the wave propagation inside the waveguide. A direct application of the effect is a phase shifter, demonstrated experimentally and by numerical simulations. Additionally, an antenna array of two dielectric waveguides, one covered in SWCNTs, is designed and fabricated. The proof-of-concept illustrates optically-controlled beam steering enabled by carbon nanotubes, and directions for further device optimizations are provided. These findings demonstrate thin SWCNT layers as an optically-reconfigurable element, suitable for broadband millimeter-wave communications.