Hey there, Angela!
You can definitely do this :)
First, navigate to your shop and start by adding all items the customer would like to order, to the cart. Next, proceed to the checkout and abandon the order!
Go into the admin orders tab then hit the "Abandoned Checkouts" in the top right, click on the order you abandoned and copy the link to send to your customer, like this.
Hope that helps!
do they have to have a created an account? I was wondering if I could go and add items to the cart for a customer and then send them the link to the cart and from there they could create and account and pay.
Have you tried creating draft orders and sending them to customers for payment: https://help.shopify.com/en/manual/orders/create-orders
The only issue with this method is the customer cannot change the orderlines so they would need to contact you to edit order or create a new order with changes.