Acoustoelectric (AE) imaging can potentially image biological currents at high spatial (~mm) and temporal (~ms) resolution. However, it does not directly map the current field distribution due to signal modulation by the acoustic field and electric lead fields. Here we present a new method for current source density (CSD) imaging. The fundamental AE equation is inverted using truncated singular value decomposition (TSVD) combined with Tikhonov regularization, where the optimal regularization parameter is found based on a modified L-curve criterion with TSVD. After deconvolution of acoustic fields, the current field can be directly reconstructed from lead field projections and the CSD image computed from the divergence of that field. A cube phantom model with a single dipole source was used for both simulation and bench-top phantom studies, where 2D AE signals generated by a 0.6 MHz 1.5D array transducer were recorded by orthogonal leads in a 3D Cartesian coordinate system. In simulations, the CSD reconstruction had significantly improved image quality and current source localization compared to AE images, and performance further improved as the fractional bandwidth (BW) increased. Similar results were obtained in the phantom with a time-varying current injected. Finally, a feasibility study using an in vivo swine heart model showed that optimally reconstructed CSD images better localized the current source than AE images over the cardiac cycle.