The dialogue-based relation extraction (DialogRE) task aims to predict the relations between argument pairs that appear in dialogue. Most previous studies utilize fine-tuning pre-trained language models (PLMs) only with extensive features to supplement the low information density of the dialogue by multiple speakers. To effectively exploit inherent knowledge of PLMs without extra layers and consider scattered semantic cues on the relation between the arguments, we propose a Guiding model with RelAtional Semantics using Prompt (GRASP). We adopt a prompt-based fine-tuning approach and capture relational semantic clues of a given dialogue with 1) an argument-aware prompt marker strategy and 2) the relational clue detection task. In the experiments, GRASP achieves state-of-the-art performance in terms of both F1 and F1c scores on a DialogRE dataset even though our method only leverages PLMs without adding any extra layers.