In this paper we deal with the initialization problem of a visual-inertial odometry system with rolling shutter cameras. Initialization is a prerequisite for using inertial signals and fusing them with visual data. We propose a novel statistical solution to the initialization problem on visual and inertial data simultaneously, by casting it into the renormalization scheme of Kanatani. The renormalization is an optimization scheme which intends to reduce the inherent statistical bias of common linear systems. We derive and present the necessary steps and methodology specific to the initialization problem. Extensive evaluations on ground truth exhibit superior performance and a gain in accuracy of up to $20\%$ over the originally proposed Least Squares solution. The renormalization performs similarly to the optimal Maximum Likelihood estimate, despite arriving at the solution by different means. With this paper we are adding to the set of Computer Vision problems which can be cast into the renormalization scheme.