We present a photometric catalogue of star cluster candidates in Hickson compact groups (HCGs) 7, 31, 42, 59, and 92, based on observations with the Advanced Camera for Surveys and the Wide Field Camera 3 on the Hubble Space Telescope. The catalogue contains precise cluster positions (right ascension and declination), magnitudes, and colours in the BVI filters. The number of detected sources ranges from 2200 to 5600 per group, from which we construct the high-confidence sample by applying a number of criteria designed to reduce foreground and background contaminants. Furthermore, the high-confidence cluster candidates for each of the 16 galaxies in our sample are split into two subpopulations: one that may contain young star clusters and one that is dominated by globular older clusters. The ratio of young star cluster to globular cluster candidates varies from group to group, from equal numbers to the extreme of HCG 31 which has a ratio of 8 to 1, due to a recent starburst induced by interactions in the group. We find that the number of blue clusters with MV < -9 correlates well with the current star formation rate in an individual galaxy, while the number of globular cluster candidates with MV < -7.8 correlates well (though with large scatter) with the stellar mass. Analyses of the high-confidence sample presented in this paper show that star clusters can be successfully used to infer the gross star formation history of the host groups and therefore determine their placement in a proposed evolutionary sequence for compact galaxy groups.