Online auction is a cornerstone of e-commerce, and a key challenge is designing incentive-compatible mechanisms that maximize expected revenue. Existing approaches often assume known bidder value distributions and fixed sets of bidders and items, but these assumptions rarely hold in real-world settings where bidder values are unknown, and the number of future participants is uncertain. In this paper, we introduce the Conformal Online Auction Design (COAD), a novel mechanism that maximizes revenue by quantifying uncertainty in bidder values without relying on known distributions. COAD incorporates both bidder and item features, using historical data to design an incentive-compatible mechanism for online auctions. Unlike traditional methods, COAD leverages distribution-free uncertainty quantification techniques and integrates machine learning methods, such as random forests, kernel methods, and deep neural networks, to predict bidder values while ensuring revenue guarantees. Moreover, COAD introduces bidder-specific reserve prices, based on the lower confidence bounds of bidder valuations, contrasting with the single reserve prices commonly used in the literature. We demonstrate the practical effectiveness of COAD through an application to real-world eBay auction data. Theoretical results and extensive simulation studies further validate the properties of our approach.