X-ray phase contrast imaging (XPCI) is a nondestructive evaluation technique that enables high-contrast detection of low-attenuation materials that are largely transparent in traditional radiography. Extending a grating-based Talbot-Lau XPCI system to three-dimensional imaging with computed tomography (CT) imposes two motion requirements: the analyzer grating must translate transverse to the optical axis to capture image sets for XPCI reconstruction, and the sample must rotate to capture angular data for CT reconstruction. The acquisition algorithm choice determines the order of movement and positioning of the two stages. The choice of the image acquisition algorithm for XPCI CT is instrumental to collecting high fidelity data for reconstruction. We investigate how data acquisition influences XPCI CT by comparing two simple data acquisition algorithms and determine that capturing a full phase-stepping image set for a CT projection before rotating the sample results in higher quality data.