We searched for {gamma}-ray blazar candidates among the 382 unidentified hard X-ray sources of the third Palermo BAT Catalog (3PBC) obtained from the analysis of 66 months of Swift Burst Alert Telescope (BAT) survey data and listing 1586 sources. We adopted a recently developed association method based on the peculiar infrared colors that characterize the {gamma}-ray blazars included in the second catalog of active galactic nuclei detected by the Fermi Large Area Telescope. We used this method exploiting the data of the all-sky survey performed by the Wide-field Infrared Survey Explorer (WISE) to establish correspondences between unidentified 3PBC sources and WISE {gamma}-ray blazar candidates located within the BAT positional uncertainty region at a 99% confidence level. We obtained a preliminary list of candidates for which we analyzed all the available data in the Swift archive to complement the information in the literature and in the radio, infrared, and optical catalogs with the information on their optical-UV and soft X-ray emission. Requiring the presence of radio and soft X-ray counterparts consistent with the infrared positions of the selected WISE sources, as well as a blazar-like radio morphology, we finally obtained a list of 24 {gamma}-ray blazar candidates.