Both can be correct. Poor farmers are deserting their fields and coming here to look for jobs - the farmers are 'doing' something. This sentence makes it seem that the farmers are looking for jobs, but may be doing other things as well or have stopped looking for jobs and doing something else. Poor farmers are deserting their fields and coming here, looking for jobs - the farmers are 'right now doing' something. This sentence makes it seem the farmers are currently still looking for a job. ~ing makes the verb progressive (doing something continually) However, to English speakers, in everyday conversation/ writing, they mean the same thing. Grammar just makes the nuance a little different. But we understand in both sentences that poor farmers are leaving their fields and going to where you live to find jobs.

"to look" is the correct answer because it expresses their purpose.