In 1992, Ortiz formed Latino Actors Base with 13 other Latino actors to provide themselves with a place to work and an opportunity to become a tightly knit ensemble. Today, that ensemble is known as LAByrinth Theater Company: an award winning troupe of over 100 artists from a wide range of cultural backgrounds and creative disciplines.

With LAByrinth, he most recently played the role of Clyde in the world premiere of Jack Goes Boating by Bob Glaudini (Drama Desk nomination). In 2006 he appeared as Che Guevara in the world premiere of School of the Americas by Jose Rivera, a co-production between LAByrinth Theater Company and The Public Theater. Other co-productions between LAByrinth and the Public include the role of Jesus in the world premiere of The Last Days of Judas Iscariot by Stephen Adly Guirgis, and José Solo in Guinea Pig Solo by Brett C. Leonard. Other LAByrinth Theater credits include Jesus Hopped the A Train by Stephen Adly Guirgis in London and New York (Drama Desk nomination, Drama League Award) and Where's My Money? written and directed by John Patrick Shanley.

In 2003, Ortiz made his Broadway debut in Nilo Cruz’ Pulitzer Prize winning play Anna in the Tropics. He appeared in three world premiere plays by José Rivera: The Adoration of the Old Woman at La Jolla Playhouse, Sueño at MCC Theater and The Street of the Sun at Mark Taper Forum. He was also featured in two New York premieres of Rivera's plays: References to Salvador Dalí Make Me Hot at the Public Theater (OBIE Award) and Cloud Tectonics at Playwrights Horizons. Ortiz also appeared in The Skin of Our Teeth and De Donde at the Public Theater; the world tours of The Merchant of Venice and The Persians directed by Peter Sellars; House Arrest at Arena Stage; and the national tour of A Few Good Men; Pentecost at Yale Repertory Theatre.

He appears in the feature films Aliens vs. Predator: Requiem, Pride and Glory, Two Lovers, Public Enemies and Fast & Furious, and he is scheduled to begin filming the screen adaptation of Jack Goes Boating, directed by Phillip Seymour Hoffman, in January 2009. In Summer 2009, he will star on stage in Othello at the Vienna Festival.