Is there a way to include a minimum order charge in pricing?

There currently isn't a way to force a minimum amount in the shopping cart.
We do offer the ability to set a Minimum Price for the product items under the items Pricing tab.
Also, you could set a range in your payment methods. You would set the Min Range to your minimum order charge on all the sites enable payment methods.
If the order amount was less than the 'minimum order charge', the user would have no payment methods shown at checkout. You would then add instructions to the checkout page, letting customers know there is an order minimum to checkout. You can add these instructions under Sites > [site name] > Settings > Instructions tab > Checkout Page Instructions.