Alarcón was born in Wilmington, California and had four brothers and two sisters. He moved to Guadalajara, Mexico with his family when he was 6 and then moved back to California when he was eighteen. Alarcón felt that he became a writer when he was fifteen and helped transcribe his grandmother's own ballad-like songs. His grandmother was a native speaker of Nahuatl. Growing up in both the United States and Mexico and experiencing both cultures helped shape the kind of writing he would create.
As a young adult, he moved back to the Los Angeles area. He received his high school diploma from Cambria Adult School. He worked in restaurants and as a migrant farm worker. During this time, he went to East Los Angeles College.
Alarcón graduated from California State University, Long Beach, and Stanford University. During college, he started writing poetry, belonged to many literary circles in the area and also read his poetry out loud at various venues. At Stanford, between 1978 and 1980, he edited the journal Vortice. In 1982, while on a Fulbright Fellowship to Mexico City, Alarcón discovered Aztec incantations translated by a Mexican priest . These later inspired the writing in Snake Poems: An Aztec Invocation. He also met his "soul mate," Mexican poet, Elías Nandino, on his trip to Mexico City. Alarcón was very impressed with how Nandino refused to hide his homosexuality from the world. During his time in Mexico, Alarcón was involved in the theatre in Mexico City and also did a lot of research at Colegio de México. The Fulbright grant also allowed him to travel to Cuba.
In 1984, Alarcón was considered a suspect in the murder of a young man, Teddy Gomez, who was killed in Golden Gate Park. He was held in jail for some time during the investigation with his bail set at $500,000. The investigation itself was considered "discriminatory." Alarcón felt that if he had been white, he never would have been considered a suspect. Others questioned the police department's actions and felt that they were also homophobic. Legal defense funds were raised, with Margarita Luna Robles organizing and leading the cause. The amount of people who came to Alarcón's aid, visiting him in jail, speaking up on his behalf, praying for him showed how the Chicano community can come together during times of trouble. The actual murderer, William Melvin White, eventually confessed and Alarcón was cleared of all charges. Later, Alarcón sued the City of San Francisco because of the trauma the investigation caused. Alarcón was said to age visibly because of the ordeal. His book, Tattoos, reflects his experience as being a murder suspect.
Alarcón and fellow poets Juan Pablo Gutierrez and Rodrigo Reyes founded Las Cuarto Espinas, the first gay Chicano poets collective, in 1985. Together, they published a collection of poetry titled Ya Vas Carnal.