The Roman Catholic Church primarily responds to the issue of asylum seeker policy through the authority of the Magisterium.

For example:

The Roman Catholic Church responded to the issue of asylum seeker policy through the promulgation of the papal encyclical Exsul Familia.

"The migrant Holy Family of Nazareth, fleeing into Egypt, is the archetype of every refugee family. Jesus, Mary and Joseph, living in exile in Egypt to escape the fury of an evil king, are, for all times and all places, the models and protectors of every migrant, alien and refugee of whatever kind who, whether compelled by fear of persecution or by want, is forced to leave his native land, his beloved parents and relatives, his close friends, and to seek a foreign soil." 

The Holy See. (1952, August 1). Exsul Familia. Retrieved from: http://www.papalencyclicals.net/pius12/p12exsul.htm 

The 2015-16 Australian Catholic Bishops Conference was convened with the social justice statement, "For Those Who've Come Across the Seas: Justice for refugees and asylum seekers." The Chairman of the Australian Catholic Social Justice Council and Auxiliary Bishop of Melbourne, Vincent Long Van Nguyen DD, commented that this statement was formed in order to address the long-standing conflict arising over the arrival of asylum seekers in Australia.