The effect of screen viewing on children’s cognitive development has been of concern among parents and researchers. This study investigated the association between children screen time, as reported by parents, and drawing ability, and the confounding effects of socioeconomic characteristics (such as parental education, household income, migration status) and children’s competing activities (such as drawing practice, extracurricular activity, outdoor time, sleep time, time playing with parents). Participants included 7577 children aged 3.5 years (50% girls) who underwent the Draw-a-person test (McCarthy score [range = 0–12 points]) in the French nationwide Elfe birth cohort, initiated in 2011. Sex-stratified zero-inflated Poisson regression models were used. Increased screen time was associated with a higher likelihood to obtain a null score in boys (OR 1.15, 95% CI 1.07–1.23) and girls (1.13 [1.03–1.24]) and a lower score in girls only (β = − 0.02, 95% CI − 0.04; − 0.01). After adjusting for SES, associations were no longer observed, indicating that the association between screen time and drawing abilities was confounded by socioeconomic characteristics.