Context. Blazars are powerful active galactic nuclei (AGNs) radiating prominently in the whole electromagnetic spectrum, from the radio to the X-ray and gamma-ray bands. Their emission is dominated by synchrotron and inverse-Compton radiation from a relativistic jet originating from an accreting central supermassive black hole. The object IGR J12319-0749 has recently been identified as a soft gamma-ray source with the IBIS instrument of the INTEGRAL satellite, coincident with a quasar at high redshift (z=3.12). Aims. We studied the radio structure of IGR J12319-0749 to strengthen its blazar identification by detecting a compact radio jet on the milli-arcsecond (mas) angular scale, and to measure its astrometric position accurate to mas level. Methods. We used the technique of electronic very long baseline interferometry (e-VLBI) to image IGR J12319-0749 with the European VLBI Network (EVN) at 5 GHz on 2012 June 19. Results. IGR J12319-0749 (J1231-0747) is a compact radio source, practically unresolved on interferometric baselines up to ~136 million wavelengths. The estimated brightness temperature (at least ~2 x 10^12 K) indicates that the radio emission of its jet is Doppler-boosted. The accurate position of the compact radio source is consistent with the positions measured at higher energies.