Yes, Jains generally can eat turmeric.

In Jain dietary practice, turmeric is considered a root/underground vegetable-like substance in many traditional classifications, and root vegetables are avoided in Jainism because they involve harming the entire plant and can contain many lives. So the important point is:

• Turmeric powder used as a spice: often accepted by many Jains in practice.
• Fresh turmeric root: generally avoided, because it is a root.

Different Jain traditions and families may follow this with some variation, so the exact practice can differ.