I have a color image and I know geographic coordinates of its 4 corners. Now I'd like to place this image on basemap in GMT using any projection. Any idea how to do that?
The process that you need to do in order to reproject your image is called georeferencing. For basic/linear georeferencing, the minimum number of points you need is 3 so if you have 4 corners you should be fine.
There's a few tutorials available on the net based on Arc and QGIS tools that can show you how to perform this on raster images. I've never used Generic Mapping Tools, so I can't say whether GMT has that functionality, but if you're using QGIS at all I'd suggest you check out this walkthrough as the process is relatively simple to perform:
Hope that helps,