Crickets are known to be a promising alternative protein source. However, a negative consumer bias and an off-flavor have become obstacles to the use of these insects in the food industry. In this study, we extracted the protein from commercial cricket powder by employing alkaline extraction–acid precipitation and including ammonium sulfate. The physicochemical and functional properties of the proteins were determined. It was found that, upon including 60% ammonium sulfate, the cricket protein isolate (CPI) had the highest protein content (~94%, w/w). The circular dichroism results indicated that a higher amount of ammonium sulfate drastically changed the secondary structure of the CPI by decreasing its α-helix content and enhancing its surface hydrophobicity. The lowest solubility of CPI was observed at pH 5. The CPI also showed better foaming properties and oil-holding capacity (OHC) compared with the cricket powder. In conclusion, adding ammonium sulfate affected the physicochemical and functional properties of the CPI, allowing it to be used as an alternative protein in protein-enriched foods and beverages.