The ALMA CMZ Exploration Survey (ACES) is an Atacama Large Millimeter/sub-millimeter Array (ALMA) large program that aims to investigate the physics driving mass flows throughout the center region of the Milky Way. We present the ACES continuum compact source catalog for dust emission in the Central Molecular Zone (CMZ) of the Galaxy. This catalog is generated from the ACES 3mm dust continuum mosaic, which spans the entire area (~7400 pc^2) of the CMZ at the high spatial resolution of ~.1.5’’ (~0.06 pc). Compact sources are extracted using a pruned dendrogram algorithm approach, generating both a complete and robust catalog of all continuum sources in the ACES mosaic. We report on the physical properties of all sources, including their flux, size, surface density, and mass. The ACES compact source catalog is the most complete census of the population of dense protostellar cores within the inner 200 pc of the Galaxy, making it a crucial starting point for defining the mass distribution of the CMZ at sub-parsec scales, and exploring the star formation properties of this dynamic region.