We present ultraviolet spectropolarimetry of the BL Lac objects OJ 287 and 0754+ 100 (OI 090.4) acquired with the Faint Object Spectrograph of the Hubble Space Telescope. These are the first such observations of radio-selected BL Lac objects and the polarimetry spans the wavelength range 1580-3300 angstrom in the observer's frame. Neither object exhibited emission-line features in their UV spectra. OJ 287 was very faint during the UV observations (V approximately 16). The UV linear polarization of this object was approximately 20%. There is no indication that the degree of polarization or the polarization position angle varies with wavelength. Nearly simultaneous optical ground-based measurements show that the polarization does not significantly change with wavelength out to approximately 8000 angstrom. The UV and optical polarization of 0754 + 100 was approximately 8% and also wavelength-independent during the epoch of observation. These observations confirm that the synchrotron emission that dominates the optical continuum also dominates in the ultraviolet in these two BL Lac objects. There is no evidence for significant contributions to the UV/optical flux by other emission components, and we set limits on the brightness of nonsynchrotron continuum components.