Yes. Cursor's download page offers Linux builds as .deb and .rpm installer files and as an AppImage, for both ordinary 64-bit PCs and ARM machines.
Cursor by Anysphere · Coding · Has a Linux version
Cursor ships for Linux at the same version as the Windows build. The download page lists installer files
for Ubuntu and Debian systems, files for Fedora and Red Hat systems, and an AppImage, which is a single
file you mark as runnable and then open, with nothing to install.
Because Cursor is built on the same foundation as Visual Studio Code, the layout, the keyboard shortcuts
and most extensions carry over from your Windows setup. Signing in with your account brings your settings
and your subscription with you.
The AI features behave the same on Linux, because that work happens on Cursor's servers rather than on your
machine, so an older or slower computer makes no difference to them. What you do need is a steady internet
connection, exactly as on Windows.