To identify long-period variable (LPV) stars in IC 10—the nearest starburst galaxy of the Local Group—we conducted an optical monitoring survey using the 2.5 m Isaac Newton Telescope with the wide-field camera (WFC) in the i band and V band from 2015 to 2017. We created a photometric catalog for 53,579 stars within the area of CCD4 of WFC (∼0.07 deg2 corresponding to 13.5 kpc2 at the distance of IC 10), of which we classified 536 and 380 stars as LPV candidates, mostly asymptotic giant branch (AGBs) stars and red supergiants, within CCD4 and two half-light radii of IC 10, respectively. By comparing our output catalog to the catalogs from Pan-STARRS, Spitzer Space Telescope, Hubble Space Telescope (HST), and carbon stars from the Canada–France–Hawai'i Telescope survey, we determined the success of our detection method. We recovered ∼73% of Spitzer's sources in our catalog and demonstrated that our survey successfully identified 43% of the variable stars found with Spitzer, and also retrieved 40% of the extremely dusty AGB stars among the Spitzer variables. In addition, we successfully identified ∼70% of HST variables in our catalog. Furthermore, we found all the confirmed LPVs that Gaia DR3 detected in IC 10 among our identified LPVs. This paper is the first in a series on IC 10, presenting the variable star survey methodology and the photometric catalog, available to the public through the Centre de Données Astronomiques de Strasbourg.