  It is clearly important to pursue atomic standards for quantities like
electromagnetic fields, time, length and gravity. We have recently shown, using
Rydberg states, that Rb atoms in a vapor cell can serve as a practical, compact
standard for microwave electric field strength. Here, we demonstrate, for the
first time, that Rb atoms excited in a vapor cell can also be used for vector
microwave electrometry by using Rydberg atom electromagnetically induced
transparency. We describe the measurements necessary to obtain an arbitrary
microwave electric field polarization at a resolution of $0.5^\circ$. The
experiments are compared to theory and found to be in excellent agreement.
