Just wrap your list inside Re (real part):
ListPointPlot3D@
Re[{{3.52169 + 1.34532^-7 I, 3.68579 - 1.28543^-7 I,
7.37118}, {3.53044, 3.69593, 7.38528}, {3.55458, 3.72804,
7.41757}, {3.59073, 3.78437, 7.47804}, {3.63526, 3.86676,
7.56669}, {3.68434, 3.97663, 7.6735}, {3.73397, 4.11494,
7.81846}, {3.78007, 4.28221, 7.98153}, {3.81847, 4.47845,
8.1727}, {3.845, 4.70322, 8.41194}, {3.85555, 4.95558,
8.6892}, {3.84609, 5.23413, 9.00446}, {3.81272, 5.53699,
9.37767}, {3.75176, 5.86187, 9.84878}, {3.65975, 6.206,
10.4778}, {3.53352, 6.56625, 11.9345 - 0.15 I}}]
