In vitro alternative therapy of human epidermoid squamous carcinoma (A431) by superparamagnetic hyperthermia (SPMHT) using Fe3O4 (magnetite) superparamagnetic nanoparticles (SPIONs) with an average diameter of 15.8 nm, bioconjugated with hydroxypropyl gamma-cyclodextrins (HP-γ-CDs) by means of polyacrylic acid (PAA) biopolymer, is presented in this paper. The therapy was carried out at a temperature of 43 °C for 30 min using the concentrations of Fe3O4 ferrimagnetic nanoparticles from nanobioconjugates of 1, 5, and 10 mg/mL nanoparticles in cell suspension, which were previously found by us to be non-toxic for healthy cells (cell viabilities close to 100%), according to ISO standards (cell viability must be greater than 70%). The temperature for the in vitro therapy was obtained by the safe application (without exceeding the biological limit and cellular damage) of an alternating magnetic field with a frequency of 312.4 kHz and amplitudes of 168, 208, and 370 G, depending on the concentration of the magnetic nanoparticles. The optimal concentration of magnetic nanoparticles in suspension was found experimentally. The results obtained after the treatment show its high effectiveness in destroying the A431 tumor cells, up to 83%, with the possibility of increasing even more, which demonstrates the viability of the SPMHT method with Fe3O4-PAA–(HP-γ-CDs) nanobioconjugates for human squamous cancer therapy.