Autistic individuals often exhibit motor atypicalities, which may relate to difficulties in social communication. This study utilized a smart tablet activity to computationally characterize motor control by testing adherence to the two-thirds power law (2/3 PL), which captures a systematic covariation between velocity and curvature in motor execution and governs many forms of human movement. Children aged 4-8 years old participated in this study, including 24 autistic children and 33 typically developing children. Participants drew and traced ellipses on an iPad. We extracted data from finger movements on the screen, and computed adherence to the 2/3 PL and other kinematic metrics. Measures of cognitive and motor functioning were also collected. In comparison to the typically developing group, the autistic group demonstrated greater velocity modulation between curved and straight sections of movement, increased levels of acceleration and jerk, and greater intra- and inter-individual variability across several kinematic variables. Further, significant motor control development was observed in typically developing children, but not in those with autism. This study is the first to examine motor control adherence to the 2/3 PL in autistic children, revealing overall diminished motor control. Less smooth, more varied movement and an indication of developmental stasis in autistic children were observed. This study offers a novel tool for computational characterization of the autism motor signature in children's development, demonstrating how smart tablet technology enables accessible assessment of children's motor performance in an objective, quantifiable and scalable manner.