We consider direction-finding in partly calibrated arrays composed of multiple identically oriented subarrays. The subarrays are assumed to possess a shift invariance structure that can be exploited for search free direction of arrival (DoA) estimation. We propose a fully distributed DoA estimation scheme that is based on the averaging consensus algorithm, in which the subarrays communicate only locally with their neighboring subarrays to exchange local averages of their measurements and received signal to iteratively compute global estimates in the network. The proposed scheme eliminates communication bottlenecks and the need for a centralized computation center. Our algorithm is based on subspace methods which is originally devised for DoA estimation in centralized systems. We show that in our fully distributed DoA estimation scheme, the number of jointly estimated directions can be larger than the number identifiable by each individual subarray.