We present a catalogue of ALMA flux density measurements of 754 calibrators observed between 2012 August and 2017 September, for a total of 16263 observations in different bands and epochs. The flux densities were measured by reprocessing the ALMA images generated in the framework of the ALMACAL project, with a new code developed by the Italian node of the European ALMA Regional Centre. A search in the online data bases yielded redshift measurements for 589 sources (̃78 per cent of the total). Almost all sources are flat spectrum, based on their low-frequency spectral index, and have properties consistent with being blazars of different types. To illustrate the properties of the sample, we show the redshift and flux density distributions as well as the distributions of the number of observations of individual sources and of timespans in the source frame for sources observed in bands 3 (84-116 GHz) and 6 (211-275 GHz). As examples of the scientific investigations allowed by the catalogue, we briefly discuss the variability properties of our sources in ALMA bands 3 and 6 and the frequency spectra between the effective frequencies of these bands. We find that the median variability index steadily increases with the source-frame time lag increasing from 100 to 800 d, and that the frequency spectra of BL Lacs are significantly flatter than those of flat-spectrum radio quasars. We also show the global spectral energy distributions of our sources over 17 orders of magnitude in frequency....