According to American Green Card "
The green card is officially known as the Alien Registration Receipt Card. The first green cards were white and were the product of the Alien Registration Act of 1940. Originally passed as a national defense measure, the act required all aliens to register themselves with the government. They could do this at the post offices, and their registration forms were forwarded to the Immigration and Naturalization Service, or the INS. However, the Alien Registration Act did not discriminate against legal and illegal immigrants. All were legal, and all were registered. After the INS processed the forms, the immigrants were sent a receipt form, and in essence, these were the first green cards to be issued.
When World War II ended and immigration once again resumed on a large scale, alien registration was not done at the post offices any more but became part of the normal procedure of immigration, and each type of immigrant was classified by a different permit. This enabled the INS to deal with far less forms and to deal the immigrants with better efficiency. And that then, is where the green card came from. There were several different types of immigrants; workers, students and teachers, and each had a registration permit that showed their status. Those immigrants, who were lucky enough to obtain a permit for permanent residence in the United States, got a green receipt, or, in other words, a green card."
This work was cited from American Green Card .com