No. There is no uTorrent desktop app for Linux. qBittorrent does the same job, it is free, it has no adverts, and it is in every Linux app store.
uTorrent by BitTorrent · Utilities · No way to run it
BitTorrent's downloads page offers uTorrent Classic for Windows and Mac, and uTorrent Web for Windows and
Mac. There is a Linux entry as well, limited to Debian and Ubuntu, but it is a separate thing rather than the
program you know from Windows, and it is not what Linux users install.
qBittorrent is what they install instead. It was written to look and behave like the old uTorrent, so the
layout of the transfer list, the categories down the side and the settings will all feel familiar within a
few minutes. It is free and open source, and unlike uTorrent it carries no adverts and no bundled offers.
Your downloads in progress can come with you. Copy the partly downloaded files and the torrent files across
and add them again in qBittorrent, pointing it at the same folder, and it will check what is already there
rather than starting from nothing. Finished downloads are ordinary files and need nothing done to them.
A word of caution that applies on any system. Downloading things you have not paid for is against the law in
Australia and most other places, and switching to Linux changes nothing about that.
Deliberately laid out like uTorrent, free, and with no adverts or bundled extras. Almost nothing to relearn.
Your files: Add your existing torrent files and point it at the same download folder, and part-finished downloads carry on.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need uTorrent. Everything else you do can move.