Yes. FarmersWeb Unlimited account type has this functionality. The buyer must already have a FarmersWeb account. Once you give this buyer terms, they'll be able to order from you online but make payment offline.
Your FarmersWeb Unlimited account is by default set up to receive terms requests. You can see your terms settings by selecting Buyer Terms from the dropdown menu in the upper right hand corner of the screen. The box below "Currently accepting offline payments" will be check marked. To disable terms, uncheck the box. If you disable terms payments, make sure to enable credit card payments, otherwise buyers will have no way of checking out for your products.
To initiate terms or accept terms requests from buyers, select Buyer Terms from the settings dropdown menu in upper right hand corner of the screen. Click the "New Terms Agreement" button and enter the buyer name (which will auto-fill from your known customer list) and select accept. This buyer can now place orders from you online but send payment offline.
You can set a default terms length at the top of the page or give any buyer custom term lengths. To give a buyer custom terms adjust the number under the "Days Until Payment Due" header to the right of the buyer name. Any buyers not given custom terms and any orders created by the seller will have the set default terms applied.
Buyers can also request terms from you. You'll see an alert on the dashboard, as well as an alert in the dropdown menu next to buyer terms when one does, and can accept or decline their request from this same page as well as edit any existing buyer terms.
All buyers you have given terms will be able to place orders from you on FarmersWeb without entering a credit card. You may then collect payment from them however you wish. You will still be able to mark their orders as paid in your Financials section to keep track of records.