Referring Expression Comprehension (REC) aims to ground the target object based on a given referring expression, which requires expensive instance-level annotations for training. To address this issue, recent advances explore an efficient one-stage weakly supervised REC model called RefCLIP. Particularly, RefCLIP utilizes anchor features of pre-trained one-stage detection networks to represent candidate objects and conducts anchor-text ranking to locate the referent. Despite the effectiveness, we identify that visual semantics of RefCLIP are ambiguous and insufficient for weakly supervised REC modeling. To address this issue, we propose a novel method that enriches visual semantics with various prompt information, called anchor-based prompt learning (APL). Specifically, APL contains an innovative anchor-based prompt encoder (APE) to produce discriminative prompts covering three aspects of REC modeling, e.g., position, color and category. These prompts are dynamically fused into anchor features to improve the visual description power. In addition, we propose two novel auxiliary objectives to achieve accurate vision-language alignment in APL, namely text reconstruction loss and visual alignment loss. To validate APL, we conduct extensive experiments on four REC benchmarks, namely RefCOCO, RefCOCO+, RefCOCOg and ReferIt. Experimental results not only show the state-of-the-art performance of APL against existing methods on four benchmarks, e.g., +6.44% over RefCLIP on RefCOCO, but also confirm its strong generalization ability on weakly supervised referring expression segmentation. Source codes are anonymously released at: https://anonymous.4open.science/r/APL-B297.