Evaluating the quality of arguments is a crucial aspect of any system leveraging argument mining. However, it is a challenge to obtain reliable and consistent annotations regarding argument quality, as this usually requires domain-specific expertise of the annotators. Even among experts, the assessment of argument quality is often inconsistent due to the inherent subjectivity of this task. In this paper, we study the potential of using state-of-the-art large language models (LLMs) as proxies for argument quality annotators. To assess the capability of LLMs in this regard, we analyze the agreement between model, human expert, and human novice annotators based on an established taxonomy of argument quality dimensions. Our findings highlight that LLMs can produce consistent annotations, with a moderately high agreement with human experts across most of the quality dimensions. Moreover, we show that using LLMs as additional annotators can significantly improve the agreement between annotators. These results suggest that LLMs can serve as a valuable tool for automated argument quality assessment, thus streamlining and accelerating the evaluation of large argument datasets.