Boric acid is an acid because its molecule

When boric acid B(OH)₃ reacts with H₂O, it accepts a hydroxyl ion from water and releases protons. It acts as an acid.

$\mathrm{B}(\mathrm{OH}{)}_3+{\mathrm{H}}_2\mathrm{O}\to \mathrm{B}(\mathrm{OH}{)}_4^{-}+{\mathrm{H}}^{+}$