We present a method of quantitatively acquiring a large complex field, containing not only amplitude information but also phase information, based on single-shot phase imaging with a coded aperture (SPICA). In SPICA, the propagating field from an object illuminated by partially coherent visible light is sieved by a coded mask, and the sieved field propagates to an image sensor, where it is captured. The sieved field is recovered from the single captured intensity image via a phase retrieval algorithm with an amplitude support constraint using the mask pattern, and then the object's complex field is reconstructed from the recovered sieved field by an algorithm employing a sparsity constraint based on compressive sensing. The system model and the theoretical bounds of SPICA are derived. We also verified the concept with numerical demonstrations.