We propose PICASSO, a novel framework CAD sketch parameterization from hand-drawn or precise sketch images via rendering self-supervision. Given a drawing of a CAD sketch, the proposed framework turns it into parametric primitives that can be imported into CAD software. Compared to existing methods, PICASSO enables the learning of parametric CAD sketches from either precise or hand-drawn sketch images, even in cases where annotations at the parameter level are scarce or unavailable. This is achieved by leveraging the geometric characteristics of sketches as a learning cue to pre-train a CAD parameterization network. Specifically, PICASSO comprises two primary components: (1) a Sketch Parameterization Network (SPN) that predicts a series of parametric primitives from CAD sketch images, and (2) a Sketch Rendering Network (SRN) that renders parametric CAD sketches in a differentiable manner. SRN facilitates the computation of a image-to-image loss, which can be utilized to pre-train SPN, thereby enabling zero- and few-shot learning scenarios for the parameterization of hand-drawn sketches. Extensive evaluation on the widely used SketchGraphs dataset validates the effectiveness of the proposed framework.