PurposeMost existing methods for accelerated parallel imaging in MRI require additional data, which are used to derive information about the sensitivity profile of each radiofrequency (RF) channel. In this work, a method is presented to avoid the acquisition of separate coil calibration data for accelerated Cartesian trajectories.MethodsQuadratic phase is imparted to the image to spread the signals in k‐space (aka phase scrambling). By rewriting the Fourier transform as a convolution operation, a window can be introduced to the convolved chirp function, allowing a low‐resolution image to be reconstructed from phase‐scrambled data without prominent aliasing. This image (for each RF channel) can be used to derive coil sensitivities to drive existing parallel imaging techniques. As a proof of concept, the quadratic phase was applied by introducing an offset to the x2 − y2 shim and the data were reconstructed using adapted versions of the image space–based sensitivity encoding and GeneRalized Autocalibrating Partially Parallel Acquisitions algorithms.ResultsThe method is demonstrated in a phantom (1 × 2, 1 × 3, and 2 × 2 acceleration) and in vivo (2 × 2 acceleration) using a 3D gradient echo acquisition.ConclusionPhase scrambling can be used to perform parallel imaging acceleration without acquisition of separate coil calibration data, demonstrated here for a 3D‐Cartesian trajectory. Further research is required to prove the applicability to other 2D and 3D sampling schemes. Magn Reson Med 73:1407–1419, 2015. © 2014 Wiley Periodicals, Inc.