$\because$点$C$是线段$AB$的黄金分割点$\left(AC \gt BC\right)$，

$\therefore AC=\dfrac{\sqrt {5}- 1}{2}AB$，

而$AB=2cm$，

$\therefore AC=\dfrac{\sqrt {5}-1}{2}\times 2=\sqrt {5}-1cm$.

故答案为$\sqrt {5}-1$.

$\because$点$C$是线段$AB$的黄金分割点$\left(AC \gt BC\right)$，

$\therefore AC=\dfrac{\sqrt {5}- 1}{2}AB$，

而$AB=2cm$，

$\therefore AC=\dfrac{\sqrt {5}-1}{2}\times 2=\sqrt {5}-1cm$.

故答案为$\sqrt {5}-1$.