There are some browser based solutions like sharedrop.io and file.pizza. I haven’t had the latter work for me though, not sure if it’s still functional. They work through WebRTC to discover local candidates for receiving files, the same way that video calling typically finds the best connection.
Security
ShareDrop uses a secure and encrypted peer-to-peer connection to transfer information about the file (its name and size) and file data itself. This means that this data is never transfered through any intermediate server but directly between the sender and recipient devices. To achieve this, ShareDrop uses a technology called WebRTC (Web Real-Time Communication), which is provided natively by browsers. You can read more about WebRTC security here.