Cardinality estimation is a fundamental functionality in database systems. Most existing cardinality estimators focus on handling predicates over numeric or categorical data. They have largely omitted an important data type, set-valued data, which frequently occur in contemporary applications such as information retrieval and recommender systems. The few existing estimators for such data either favor high-frequency elements or rely on a partial independence assumption, which limits their practical applicability. We propose ACE, an Attention-based Cardinality Estimator for estimating the cardinality of queries over set-valued data. We first design a distillation-based data encoder to condense the dataset into a compact matrix. We then design an attention-based query analyzer to capture correlations among query elements. To handle variable-sized queries, a pooling module is introduced, followed by a regression model (MLP) to generate final cardinality estimates. We evaluate ACE on three datasets with varying query element distributions, demonstrating that ACE outperforms the state-of-the-art competitors in terms of both accuracy and efficiency.