Add the chile de árbol, agave, and water to a small saucepan and set over medium heat, bring to a simmer. Lower heat to medium and let simmer for 3-5 minutes. Remove from heat, let cool to room temperature (do not refrigerate, the mixture will seize) and strain.
To make the paloma:
Rim a chilled glass with lime and salt. Add the tequila, lime juice, tangerine juice, and 1 ounce of the chile de árbol agave syrup to a shaker, add ice, and shake. Strain into the rimmed glass with ice. Top with a splash of seltzer water and garnish with a tangerine slice.