Bring water and quinoa to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until quinoa is tender and water has been absorbed, 15 to 20 minutes.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add carrots, corn, peas, and broccoli to steamer; cover, and steam until tender, 5 to 10 minutes.
Mix quinoa and vegetable mixture together in a bowl.
Whisk olive oil, lemon juice, chili powder, and cayenne pepper together in a bowl; pour over quinoa mixture and toss to coat.