A low-cost device for registration-free quantitative phase microscopy (QPM) based on the transport of intensity equation of cells in continuous flow is presented. The method uses acoustic focusing to align cells into a single plane where all cells move at a constant speed. The acoustic focusing plane is tilted with respect to the microscope’s focal plane in order to obtain cell images at multiple focal positions. As the cells are displaced at constant speed, phase maps can be generated without the need to segment and register individual objects. The proposed inclined geometry allows for the acquisition of a vertical stack without the need for any moving part, and it enables a cost-effective and robust implementation of QPM. The suitability of the solution for biological imaging is tested on blood samples, demonstrating the ability to recover the phase map of single red blood cells flowing through the microchip.