[abridged] We study the resolved stellar populations and derive the SFH of the SDIG, a gas-rich dwarf galaxy member of the NGC7793 subgroup in the Sculptor group. We construct a CMD using archival HST observations and examine its stellar content. We derive its SFH using a maximum-likelihood fit to the CMD. The CMD shows that SDIG contains stars from 10Myr to several Gyr old, as revealed from the MS, BL, luminous AGB, and RGB stars. The young stars with ages less than ~250Myr show a spatial distribution confined to its central regions, and additionally the young MS stars exhibit an off-center density peak. The intermediate-age and older stars are more spatially extended. SDIG is dominated by intermediate-age stars with an average age of 6.4Gyr. The average metallicity inferred is [M/H]\approx -1.5dex. Its SFH is consistent with a constant SFR, except for ages younger than ~200Myr. The lifetime average SFR is 1.3x10^{-3} Mo/yr. More recently than 100Myr, there has been a burst of SF at a rate ~2-3 times higher than the average SFR. The inferred recent SFR from CMD modelling is higher than inferred from the Ha flux of the galaxy; we interpret this to mean that the upper end of the IMF is not being fully sampled due to the low SFR. Additionally, an observed lack of bright blue stars in the CMD could indicate a downturn in SFR on 10^7-yr timescales. A previous SF enhancement appears to have occurred between 600-1100Myr ago, with amplitude similar to the most recent 100Myr. Older bursts of similar peak SFR and duration would not be resolvable with these data. The observed enhancements in SF suggest that SDIG is able to sustain a complex SFH without the effect of interactions with its nearest massive galaxy. Integrating the SFR over the entire history of SDIG yields a total stellar mass 1.77x10^{7}Mo, and a current V-band stellar mass-to-light ratio 3.2Mo/Lo.

A&A accepted; 10 pages, 9 figures