The discovery of giant viruses in unicellular eukaryotic hosts has raised new questions on the nature of viral life. Although many steps in the infection cycle of giant viruses have been identified, the quantitative life history traits associated with giant virus infection remain unknown or poorly constrained. In this study, we provide the first estimates of quantitative infection traits of a giant virus by tracking the infection dynamics of the bacterivorous protist Cafeteria roenbergensis and its lytic virus CroV. Leveraging mathematical models of infection, we quantitatively estimate the adsorption rate, onset of DNA replication, latency time, and burst size from time-series data. Additionally, by modulating the initial ratio of viruses to hosts, we also provide evidence of a potential MOI-dependence on adsorption and burst size. Our work provides a baseline characterization of giant virus infection dynamics relevant to ongoing efforts to understand the ecological role of giant viruses.