IRAS, COBE, and ISO have demonstrated the unique importance of a cryogenic infrared telescope in space for studying diffuse infrared backgrounds and for teasing out the individual point sources which contribute to them. This importance results from the extremely high infrared sensitivity of such telescopes, particularly to diffuse radiation. The next cryogenic infrared telescope will be NASA's Space Infrared Telescope Facility (SIRTF), which is currently in the final stages of construction leading to launch in 2002. SIRTF will be the first infrared space observatory to make extensive use - both for imaging and spectroscopy - of large format infrared detector arrays. The sensitivity and spatial and spectral coverage of SIRTF's array-based instruments endow SIRTF with great power for the study of the cosmic infrared background (CIRB) and related scientific issues. This paper reviews the SIRTF mission design and measurement functionality and describes SIRTF's potential studies of the CIRB, drawing examples from the programs planned by the SIRTF Guaranteed Time Observers (GTO's). We also summarize the opportunities for community participation in SIRTF.