The invention relates to a sulfoacid rare earth catalyst for polymerizing high-cis-isoprene rubber and a preparation method thereof. The catalyst comprises benzenesulfonic acid neodymium rare earth complex and alkyl aluminum; the molar ratio of the alkyl aluminum to the rare earth neodymium in the benzenesulfonic acid neodymium rare earth complex is 15 to 40:1, wherein the benzenesulfonic acid neodymium rare earth complex comprises benzenesulfonic acid neodymium alcohol complex, benzenesulfonic acid neodymium sulphoxide complex, benzenesulfonic acid neodymium furan complex, benzenesulfonic acid neodymium amine complex, benzenesulfonic acid neodymium ether complex and benzenesulfonic acid neodymium ester complex; ligand comprises: alcohol compound, sulfoxide compound, furan compound, amine compound, ether compound and ester compound; and the alkyl aluminum comprises: 3-isobutyl aluminum, triethyl aluminum, diisobutyl aluminum hydride, or diethyl aluminum hydride. The sulfoacid rare earth complex catalyst is used for polymerizing isoprene, and can obtain the high-cis rare earth polyisoprene rubber with the cis 1,4 structure content more than 96.0 percent and the weight-average molecular weight more than 2.2 million.