Border Security and Deferred Action Recipient Relief Act This bill establishes the Border Security Trust Fund, which shall make funds available for: (1) specified border fencing and wall procurement, construction, and improvements in Texas and California; and (2) border wall planning activities. The Department of Homeland Security (DHS) may cancel removal of, and grant lawful permanent resident status on a conditional basis for up to 10 years to, qualifying resident aliens who: (1) have been continuously physically present in the United States since January 1, 2012; (2) were under 16 years old on the initial date of U.S. entry or, if 18 years or older when filing under this bill, have met certain educational, employment, or military requirements; (3) are not inadmissible or deportable on criminal, security, terrorism, or other grounds; (4) have not participated in persecution of any person on account of race, religion, nationality, membership in a particular social group, or political opinion; and (5) have not been convicted of specified federal or state offenses. Such an alien may subsequently adjust to permanent resident status and become eligible for naturalization. DHS may designate as a criminal gang or cartel a group, club, organization, or association comprised of five or more individuals that has as a primary purpose the commission of one or more specified criminal offenses and whose members engage in, or, during the five years immediately preceding the most recent commission of such an offense, have engaged in, a continuing series of such offenses. The bill makes persons associated with gangs or cartels inadmissible or deportable. DHS shall complete the construction of roads along the southern border to facilitate U.S. Customs and Border Protection access.