The getconnectioncount RPC returns the number of connections to other nodes.
getconnectioncount none
*bitcoin-cli help getconnectioncount
getconnectioncount Returns the number of connections to other nodes. Result: n (numeric) The connection count Examples: > bitcoin-cli getconnectioncount > curl --user myusername --data-binary '{"jsonrpc": "1.0", "id":"curltest", "method": "getconnectioncount", "params": [] }' -H 'content-type: text/plain;' http://127.0.0.1:8332/