C

$\because$线段$AB=2$，点$C$是线段$AB$的黄金分割点，
$\therefore$当$AC \gt BC$时，$AC=\frac{\sqrt{5}-1}{2}AB=\frac{\sqrt{5}-1}{2}×2=\sqrt{5}-1$，
当$AC \lt BC$时，$BC=\frac{\sqrt{5}-1}{2}AB=\frac{\sqrt{5}-1}{2}×2=\sqrt{5}-1$，
$\therefore AC=AB-BC=2-(\sqrt{5}-1)=3-\sqrt{5}$.
故答案为：$\sqrt{5}-1$或$3-\sqrt{5}$.
故选：$C$.