Since line segment \( AB \) is bisected at point \( C \), the lengths of segments \( AC \) and \( CB \) will be equal. Given that \( AB = 4 \) units, we divide this length by 2 to find \( AC \):
\[ AC = \frac{AB}{2} = \frac{4}{2} = 2 \text{ units.} \]
Therefore, \( AC = 2 \) units.