In the present study, the sorption of perrhenate ions from sulfuric acid liquors was studied using three types of polymer ion exchange resins. An anion exchange resin type 1 (a copolymer of 2-methyl-5-vinylpyridine with divinylbenzene (VP-DVB)) as well as two polyfunctional resins containing anion and cation exchange functional groups, namely, type 2 (a carboxylated VP-DVB with pyridine-2-carboxylic acid (picolinic acid) functional group) and type 3 (an aminophosphorylated VP-DVB with pyridine-2-[(methylamino)methyl]phosphonic acid functional group), were studied. The resins before and after rhenium sorption were characterized by FT-IR spectroscopy and XPS spectroscopy. The incorporation of additional acidic functional groups into the polymer matrix of the VP-DVB resins led to a slight decrease in the rhenium anion exchange capacity. At the same time, polyfunctional resins make it possible to strip rhenium with hydrochloric acid. A completely new process for the preconcentration of rhenium as a halide compound, which will contribute to the low-cost production of metallic rhenium, can be implemented using these new polyfunctional resins. Column sorption experiments using real uranium leach liquors demonstrated an exchange capacity of 33.2 mg of Re per gram of resin and a concentration factor in the eluate of ∼2500. The possibility of anion exchange recovery of rhenium from uranium leach liquors by Type 3 resin followed by direct precipitation of potassium hexachlororhenate from hydrochloric acid desorption liquor was demonstrated. The present study provided a new resin for rhenium recovery with excellent adsorption and elution characteristics, which is a promising candidate for practical applications.