Accurate segmentation of anatomical structures in fetal cardiac ultrasound views is crucial for the diagnosis of congenital heart disease (CHD) in fetuses. However, this task remains highly challenging due to the small size and complex morphology of the fetal heart, as well as the presence of high noise and blurry boundaries inherent in ultrasound imaging. Existing methods typically rely on precise annotations provided by obstetric experts, which are both time-consuming and costly. To address these challenges, we propose CSP-SAM, a novel SAM-based segmentation framework specifically designed for fetal cardiac ultrasound image analysis. Specifically, we design a CNN adapter branch to enhance the spatial representation capability of the image encoder and mask decoder, enabling the model to better capture the complex anatomical features of the fetal heart. To reduce reliance on expert annotations, we propose a self-prompting strategy that autonomously generates high-quality point, box, and mask prompts for effective guidance in the segmentation process. By integrating these components into the CSP-SAM framework, our method is extensively evaluated on two public fetal cardiac ultrasound datasets and one private clinical dataset, demonstrating state-of-the-art performance compared to existing models.