This paper presents a widely-linear (WL) distributed beamforming algorithm that takes advantage of strictly second-order (SO) non-circular source signals. We consider a single-antenna source-destination pair, which is assisted by multiple relays but suffers from strong interference. Assuming that perfect channel state information (CSI) is available, we design our algorithm based on the maximization of the signal-to-interference-plus-noise ratio (SINR) under a total relay power constraint after applying WL processing. We prove that in the case of no interference, the proposed WL distributed beamforming algorithm provides an SINR gain of 3 dB over its linear counterpart due to a virtual doubling of the number of relays. Also, the complexity is analyzed and simulations for the interference scenario show the performance gains in terms of the SINR and the bit error rate (BER).