We present ALMA 97.5 GHz total intensity and linear polarization observations of the mm-band afterglow of GRB 190114C spanning 2.2 to 5.2 hours after the burst. We detect linear polarization at the $≈ 5\,σ$ level, decreasing from $Π=(0.87±0.13)\%$ to $(0.60±0.19)\%$, and evolving in polarization position angle from $(10±5)^∘$ to $(-44±12)^∘$ during the course of the observations. This represents the first detection of polarized millimeter emission in a $γ$-ray burst. We show that the optical and X-ray observations between $0.03$ days and $∼0.3$ days are consistent with a fast cooling forward shock expanding into a wind environment. However, the optical observations at $\lesssim0.03$ days, as well as the radio and millimeter observations arise from a separate component, which we interpret as emission from the reverse-shocked ejecta. Using the measured linear polarization, we constrain the coherence scale of tangled magnetic fields in the ejecta to an angular size of $θ_{\rm B} ≈10^{-3}$ radian, while the rotation of the polarization angle rules out the presence of large scale, ordered axisymmetric magnetic fields, and in particular a large scale toroidal field, in the jet.