Violet Grace Youens died after being struck on Prescot Road in St Helens, Merseyside on Friday 24 March.
Aidan McAteer, 23 and from Prescot, has also been charged with causing serious injury by dangerous driving and theft of a motor vehicle.
He appeared at Liverpool, Knowsley and St Helens Adult Remand Court.
McAteer, who wore a blue sports top and grey tracksuit bottoms, stared at the floor throughout the short hearing and gave his address as no fixed abode.
He nodded to confirm he understood the charges against him and was remanded in custody to appear at Liverpool Crown Court on 26 April.
Violet's grandmother, Angela French, who was also hit by the car, remains in hospital in a serious but stable condition, Merseyside Police said.
A man has appeared in court charged with causing death by dangerous driving after a four-year-old girl was hit and killed by a car.