The identification of low-energy counterparts for y-ray sources is one of the biggest challenges in modern y-ray astronomy. Recently, we developed and successfully applied a new association method to recognize y-ray blazar candidates that could be possible counterparts for the unidentified y-ray sources above 1--MeV in the second Fermi Large Area Telescope (LAT) catalog (2FGL). This method is based on the Infrared (IR) colors of the recent Wide-Field Infrared Survey Explorer (WISE) all-sky survey. In this letter we applied our new association method to the case of unidentified INTEGRAL sources (UISs) listed in the fourth soft gamma-ray source catalog (4IC). Only 86 UISs out of the 113 can be analyzed, due to the sky coverage of the WISE Preliminary data release. Amone these 86 UISs, we found that 18 aoppear to have a y-ray blazar candidate within their positional error region. Finally, we analyzed the Swift archival data available for 10 out of these 18 y-ray blazar candidates,, and we found that 7 out of 10 are clearly detected in soft X-rays and/or in the optical-ultraviolet band. We cannot confirm the associations between the UISs and the selected y-ray blazar candidates due to the discrepancies between the INTEGRAL and the soft X-ray spectra. However, the discovery of the soft X-ray counterparts for the selected y-ray blazar candidates adds an important clue to help understand their origin and to confirm their blazar nature. Show Partial Abstract