Towed streamer electromagnetic (TSEM) survey is an efficient data acquisition technique capable of collecting a large volume of electromagnetic (EM) data over extensive areas rapidly and economically. The TSEM survey is capable of detecting and characterizing marine hydrocarbon (HC) reservoirs. However, interpretation of the TSEM data is still a very challenging problem. We propose solving this problem by migrating the optimal synthetic aperture (OSA) data for the TSEM survey. We first represent the OSA data as a solution of Lippmann-Schwinger equation and then demonstrate that the migration of OSA data is just the inner product of the backward-propagated and forward-propagated EM fields. The migration problem is solved iteratively within the general framework of the reweighted, regularized, conjugate gradient (RRCG) method. The proposed method was tested with two synthetic models. We also applied this method to the TSEM data set collected in the Barents Sea and revealed a resistive layer at a depth of about 500 m.