We study ram pressure stripping in simulated Milky Way-like halos at z>=2 from the Figuring Out Gas & Galaxies In Enzo (FOGGIE) project. These simulations reach exquisite resolution in their circumgalactic medium (CGM) gas owing to FOGGIE's novel refinement scheme. The CGM of each halo spans a wide dynamic range in density and velocity over its volume-roughly 6 dex and 1000 km/s, respectively-translating into a 5 dex range in ram pressure imparted to interacting satellites. The ram pressure profiles of the simulated CGM are highly stochastic, owing to kpc-scale variations of the density and velocity fields of the CGM gas. As a result, the efficacy of ram pressure stripping depends strongly on the specific path a satellite takes through the CGM. The ram-pressure history of a single satellite is generally unpredictable and not well correlated with its approach vector with respect to the host galaxy. The cumulative impact of ram pressure on the simulated satellites is dominated by only a few short strong impulses-on average, 90% of the total surface momentum gained through ram pressure is imparted in 20% or less of the total orbital time. These results reveal an erratic mode of ram pressure stripping in Milky-Way like halos at high redshift-one that is not captured by a smooth spherically-averaged model of the circumgalactic medium.