Large language models (LLMs) have facilitated the generation of high-quality, cost-effective synthetic data for developing downstream models and conducting statistical analyses in various domains. However, the increased reliance on synthetic data may pose potential negative impacts. Numerous studies have demonstrated that LLM-generated synthetic data can perpetuate and even amplify societal biases and stereotypes, and produce erroneous outputs known as ``hallucinations'' that deviate from factual knowledge. In this paper, we aim to audit artifacts, such as classifiers, generators, or statistical plots, to identify those trained on or derived from synthetic data and raise user awareness, thereby reducing unexpected consequences and risks in downstream applications. To this end, we take the first step to introduce synthetic artifact auditing to assess whether a given artifact is derived from LLM-generated synthetic data. We then propose an auditing framework with three methods including metric-based auditing, tuning-based auditing, and classification-based auditing. These methods operate without requiring the artifact owner to disclose proprietary training details. We evaluate our auditing framework on three text classification tasks, two text summarization tasks, and two data visualization tasks across three training scenarios. Our evaluation demonstrates the effectiveness of all proposed auditing methods across all these tasks. For instance, black-box metric-based auditing can achieve an average accuracy of $0.868 \pm 0.071$ for auditing classifiers and $0.880 \pm 0.052$ for auditing generators using only 200 random queries across three scenarios. We hope our research will enhance model transparency and regulatory compliance, ensuring the ethical and responsible use of synthetic data.