Large Language Models (LLMs) have demonstrated remarkable success across a wide range of industries, primarily due to their impressive generative abilities. Yet, their potential in applications requiring cognitive abilities, such as psychological counseling, remains largely untapped. This paper investigates the key question: \textit{Can LLMs be effectively applied to psychological counseling?} To determine whether an LLM can effectively take on the role of a psychological counselor, the first step is to assess whether it meets the qualifications required for such a role, namely the ability to pass the U.S. National Counselor Certification Exam (NCE). This is because, just as a human counselor must pass a certification exam to practice, an LLM must demonstrate sufficient psychological knowledge to meet the standards required for such a role. To address this, we introduce PsychCounsel-Bench, a benchmark grounded in U.S.national counselor examinations, a licensure test for professional counselors that requires about 70\% accuracy to pass. PsychCounsel-Bench comprises approximately 2,252 carefully curated single-choice questions, crafted to require deep understanding and broad enough to cover various sub-disciplines of psychology. This benchmark provides a comprehensive assessment of an LLM's ability to function as a counselor. Our evaluation shows that advanced models such as GPT-4o, Llama3.3-70B, and Gemma3-27B achieve well above the passing threshold, while smaller open-source models (e.g., Qwen2.5-7B, Mistral-7B) remain far below it. These results suggest that only frontier LLMs are currently capable of meeting counseling exam standards, highlighting both the promise and the challenges of developing psychology-oriented LLMs. We release the proposed dataset for public use: https://github.com/cloversjtu/PsychCounsel-Bench