Despite its widespread use in fiber optics, encoding quantum information in photonic time-bin states is usually considered impractical for free-space quantum communication as turbulence-induced spatial distortion impedes the analysis of time-bin states at the receiver. Here, we demonstrate quantum key distribution using time-bin photonic states distorted by turbulence and depolarization during free-space transmission. Utilizing a novel analyzer apparatus, we observe stable quantum bit error ratios of 5.32 %, suitable for generating secure keys, despite significant wavefront distortions and polarization fluctuations across a 1.2 km channel. This shows the viability of time-bin quantum communication over long-distance free-space channels, which will simplify direct fiber/free-space interfaces and enable new approaches for practical free-space quantum communication over multi-mode, turbulent, or depolarizing channels.