Step 1: Understanding carotenoids.
$\beta$-carotene is a carotenoid pigment found in plants and fruits like carrot and mango.
Step 2: Pigment colour.
Carotenoids are responsible for yellow, orange, and red colours, and $\beta$-carotene specifically imparts an orange colour.
Step 3: Conclusion.
Therefore, the colour of $\beta$-carotene is orange.