Decentralized electronic voting solutions represent a promising advancement in electronic voting. One of the e-voting paradigms, the self-tallying scheme, offers strong protection of the voters' privacy while making the whole voting process verifiable. Decentralized smart contract platforms became interesting practical instantiation of the immutable bulletin board that this scheme requires to preserve its properties. Existing smart contract-based approaches employing the self-tallying scheme (such as OVN or BBB-Voting) are only suitable for a boardroom voting scenario due to their scalability limitation. The goal of our work is to build on existing solutions to achieve scalability without losing privacy guarantees and verifiability. We present SBvote, a blockchain-based self-tallying voting protocol that is scalable in the number of voters and therefore suitable for large-scale elections. The evaluation of our proof-of-concept implementation shows that the protocol's scalability is limited only by the underlying blockchain platform. We evaluated the scalability of SBvote on two public smart contract platforms -- Gnosis and Harmony. Despite the limitations imposed by the throughput of the blockchain platform, SBvote can accommodate elections with millions of voters.