Can "immigrant" be used to refer to a "person who moves from rural area to city"?

I have looked up the word 'immigrant': the definition refers to people who come to live in a different country. Can I also use this word to refer to people who move from rural areas to the city?

Solution 1:

No, immigrants isn't normally used for people who move within the same country from rural to urban areas. But such people are often called [economic] migrants, or more specifically...

Rural migrants are attracted by the possibilities that cities can offer, but often settle in shanty towns and experience extreme poverty. (source: Wikipedia article on urbanisation).

The relevant OED definition is...

migrant: A person who moves permanently to live in a new country, town, etc., esp. to look for work, or to take up a post, etc.; an immigrant. (italics mine)

I interpret the last two words of the definition as meaning immigrants are one kind of migrants (specifically, the kind that move to a different country).

Solution 2:

No, it's not really appropriate for that context. The word immigrant formally means, as you said:

a person who comes to a country to take up permanent residence

Someone who simply moves between locations within the same country relocates rather than immigrates. I'm having trouble finding a good noun to describe someone who specifically moves from the country to the city, however. The process as a whole is called urbanization.