Can I make HTTP requests using OpenCL in C#? I tryed to do this calling system("curl website.com") but only getting an error about system implicit calling.
No, you can't. The OpenCL kernel C/C++ language doesn't support the standard C library - this library is replaced by a custom set of standard functions, geared toward math programming.
The list of functions, which can be used in the kernel language, can be found here.