We measure the AC Zeeman force on an ultracold gas of 87 Rb due to a microwave magnetic field targeted to the 6.8 GHz hyperfine splitting of these atoms. An atom chip produces a microwave near-field with a strong amplitude gradient, and we observe a force over three times the strength of gravity. Our measurements are consistent with a simple 2-level theory for the AC Zeeman effect and demonstrate its resonant, bipolar, and spin-dependent nature. We observe that the dressed atom eigenstates gradually mix over time and have mapped out this behavior as a function of magnetic field and detuning. We demonstrate the practical spin-selectivity of the force by pushing or pulling a specific spin state while leaving other spin states unmoved.