You can use the Draft Order Endpoint if you want Shopify to calculate the tax on your behalf - it would calculate tax based on the customer address and the items.
You could then complete the Draft Order, which would convert it to an actual order.
I've also noticed the Draft Order API documentation has a mistake (I'll follow up internally about that as an aside) but here are the calls to complete a Draft Order to mark as paid/or pending. Hope that helps!
Complete and mark as paid
Complete and mark as pending
Hope this helps!