The MinGW-w64 tools from https://winlibs.com/ are only a build toolchain, so they don't contain libraries for you to link with (yet).

You need a Windows build of libcurl and use that.

To use it you must include the location to the header files using the -I compiler flag, and then link with the library by pointing to the location of the .a file with the -L linker flag and then link with the library using the -l flag (-lcurl in this case). If you don't have .a files you can also try to link with the full path of the .dll file and gcc will know it's a shared library.

An easier way is to get libcurl via MSYS2's pacman package manager. If you want to statically link you need to use the output of pkg-config --static --libs libcurl as link flags.

In practice though I noticed that sometomes pkg-config --static --libs libcurl is missing some dependencies and you still need to add some manually. An example of a project of mine that builds on Windows with winlibs MinGW-w64 (both 32-bit and 64-bit) can be found at https://github.com/brechtsanders/winlibs_tools/blob/main/Makefile (specifically look for the definition of CURL_LDFLAGS)