We present measurements of the polarization of X-rays in the 2–8 keV band from the pulsar in the ultracompact low-mass X-ray binary 4U 1626–67 using data from the Imaging X-Ray Polarimetry Explorer (IXPE). The 7.66 s pulsations were clearly detected throughout the IXPE observations as well as in the NICER soft X-ray observations, which we used as the basis for our timing analysis and to constrain the spectral shape over the 0.4–10 keV energy band. Chandra HETGS high-resolution X-ray spectra were also obtained near the times of the IXPE observations for firm spectral modeling. We found an upper limit on the pulse-averaged linear polarization of <4% (at 95% confidence). Similarly, there was no significant detection of polarized flux in pulse phase intervals when subdividing the bandpass by energy. However, spectropolarimetric modeling over the full bandpass in pulse phase intervals provided a marginal detection of polarization of the power-law spectral component at the 4.8% ± 2.3% level (90% confidence). We discuss the implications concerning the accretion geometry onto the pulsar, favoring two-component models of the pulsed emission.