Entity linking (EL) is the task of linking entity mentions in a document to referent entities in a knowledge base (KB). Many previous studies focus on Wikipedia-derived KBs. There is little work on EL over Wikidata, even though it is the most extensive crowdsourced KB. The scale of Wikidata can open up many new real-world applications, but its massive number of entities also makes EL challenging. To effectively narrow down the search space, we propose a novel candidate retrieval paradigm based on entity profiling. Wikidata entities and their textual fields are first indexed into a text search engine (e.g., Elasticsearch). During inference, given a mention and its context, we use a sequence-to-sequence (seq2seq) model to generate the profile of the target entity, which consists of its title and description. We use the profile to query the indexed search engine to retrieve candidate entities. Our approach complements the traditional approach of using a Wikipedia anchor-text dictionary, enabling us to further design a highly effective hybrid method for candidate retrieval. Combined with a simple cross-attention reranker, our complete EL framework achieves state-of-the-art results on three Wikidata-based datasets and strong performance on TACKBP-2010.