In this paper, a wire detection algorithm is proposed for synthetic aperture radar (SAR) images. The algorithm is specifically designed for SAR images generated from an agile, drone-mounted, omnidirectional radar array to be used for the detection of improvised explosive devices (IEDs). A multistage approach consisting of denoising, constant false alarm rate (CFAR) thresholding, feature extraction, and automated detection using the Radon transform, is proposed and applied to a set of SAR images with multiple aspect angles. At each detection step, the look-angles of individual pixels are used to remove false alarms, and improve detection accuracy. The algorithm is tested using measured data and provides an acceptable detection performance on straight wire segments even in the presence of a strong background clutter.