A random-ballistic deposition model where particles are aggregated according to the rules of ballistic deposition with probability p and following a random deposition process with probability 1-p, respectively, is proposed and studied. Based on extensive numerical simulations a dynamic scaling ansatz for the interface width W(L,t,p) as a function of lattice side L, time t and p is formulated. Three new exponents, which can be linked to the standard growth exponent of ballistic deposition by means of a new scaling relation, are identified.