You can curl some synthetic wigs, but the fiber decides the method. A regular synthetic wig can melt or permanently kink if you treat it like human hair.
First check the label
If the wig says heat-friendly, heat-defiant, or heat-resistant, you may be able to use low-temperature tools within the brand's limit. If it does not say that, assume hot tools are risky.
Safer curl methods
For regular synthetic fiber, try foam rollers, steam setting, hot water setting, or pin curls with controlled warmth instead of a curling iron.
Bottom line
A synthetic wig can be curled, but not always with a curling iron. Heat-friendly fiber gets low heat; regular synthetic gets heatless or steam-based styling.