question

You can't do this directly with only RC tools/apps, but you can do it with extra non-RC tools.   We do this exact thing for ourselves and some of our customers that use RC.  There are 3 approaches you can take:  

1) Emailed Fax Notifications - have all your fax notifications with fax attachments emailed to a specific private email account that no-one has access to.  Install a purchased or build-it-yourself app on your server that reads the email account, downloads, updates the PDF to be readable, and then saves them in your server archive.

2) API DIY App - similar to approach 1, but instead of using emails, build an API app that accesses your fax number via the RC API and directly download the faxes.   You can even register a call-back app function that RC will automatically call every time a fax is received - this way you don't have to check for faxes on a cycled period (eg. every minute, etc.).

3) Purchased App - search the app library, there are many prebuilt apps and services that extend RC functionality and many of them provide some form of improved fax management and / or archiving.  As the title indicates, this option usually costs extra (monthly, yearly, per fax line, etc.) since it is not an RC service.

( we use approach 1 for some setups and approach 2 for some others, and have not tested or used any approach 3 options, only read about them )