Before septation processes shape its four chambers, the embryonic heart is a straight tube that spontaneously bends and twists breaking the left-right symmetry. In particular, the heart tube is subjected to a cell remodeling inducing ventral bending and dextral torsion during the c-looping phase. In this work we propose a morphomechanical model for the torsion of the heart tube that behaves as a nonlinear elastic body. We hypothesize that this spontaneous looping can be modeled as a mechanical instability due to accumulation of residual stresses induced by the geometrical frustration of tissue remodeling, which mimics the cellular rearrangement within the heart tube. Thus, we perform a linear stability analysis of the resulting nonlinear elastic boundary value problem to determine the onset of c-looping as a function of the geometry of the tube and of the internal remodeling rate. We perform numerical simulations to study the fully nonlinear morphological transition, showing that the soft tube develops a realistic self-contacting looped shape in the physiological range of geometrical parameters.