Epidermal squamous cell carcinoma (SCC) is a common and highly invasive form of cancer. SCC arises due to ultraviolet light exposure and is associated with increased expression of pro-cancer genes and reduced expression of cancer suppressors. Actin-Like Protein 6A (ACTL6A, BAF53a) is an important protein subunit of the SWI/SNF epigenetic chromatin regulatory complex. ACTL6A is elevated in cancer cells and has been implicated as a driver of cancer cell proliferation and tumor growth. In the present study, we show that ACTL6A drives SCC cell proliferation, spheroid formation, invasion and migration, and that these activities are markedly reduced by ACTL6A knockdown. We further show that ACTL6A expression is associated with reduced levels of the p21Cip1 cyclin-dependent kinase inhibitor and tumor suppressor protein. Molecular studies show that ACTL6A interacts with p53 DNA response elements in the p21Cip1 gene promoter to suppress p21Cip1 promoter activity and mRNA and protein level. Additional studies show that an increase in p21Cip1 expression in ACTL6A knockdown cells is required for suppression of the SCC cell phenotype, suggesting that p21Cip1 is a mediator of ACTL6A action. We further show that this regulation is p53 independent. These findings suggest that ACTL6A suppresses p21Cip1 promoter activity to reduce p21Cip1 protein as a mechanism to maintain the aggressive epidermal SCC phenotype.