Hampus Sjöberg has set up a site (https://taproot.watch/) with a graphic for which blocks have signaled for Taproot activation and a breakdown by mining pools.
AJ Towns stated on Mastodon that once signaling starts the Bitcoin Core RPC getblockchaininfo will report the number of signaling blocks in the current period.
David Harding added on Mastodon:
If you want to implement checking yourself, you can use the versionhex in either debug.log or the results of
getblock. Taproot is using bit 2. See the versionbits FAQ for details about bits:
pox also wrote an awk script that I haven't tested.
gawk -F'[= ]' '/UpdateTip/ { print("block="$7" taproot="and($9,2)) }' <~/.bitcoin/debug.log