The super Pioneering High Energy Nuclear Interaction eXperiment (sPHENIX) at the Relativistic Heavy Ion Collider (RHIC) will perform high precision measurements of jets and heavy flavor observables for a wide selection of nuclear collision systems, elucidating the microscopic nature of strongly interacting matter ranging from nucleons to the strongly coupled quark-gluon plasma. A prototype of the sPHENIX calorimeter system was tested at the Fermilab Test Beam Facility as experiment T-1044 in the spring of 2016. The electromagnetic calorimeter (EMCal) prototype is composed of scintillating fibers embedded in a mixture of tungsten powder and epoxy. The hadronic calorimeter (HCal) prototype is composed of tilted steel plates alternating with plastic scintillator. Results of the test beam reveal the energy resolution for electrons in the EMCal is $2.8%oplus~15.5%/sqrt{E}$ and the energy resolution for hadrons in the combined EMCal plus HCal system is $13.5%oplus 64.9%/sqrt{E}$. These results demonstrate that the performance of the proposed calorimeter system satisfies the sPHENIX specifications.