Of course you can, sure servers tend to be the main clients of SANs but there's literally nothing stopping you from doing it on a workstation so long as you know what you want and how to do it.
First of all you need to decide what kind of connection you need or want to make - if it's an existing share/drive you want to connect to then you may well have to do it using the same methods - you need speak to your storage peeps about this.
If they then come back and say it's FC storage then you need to do a few things;
Add an FC HBA to your system using a spare, appropriate, PCIe slot - there are really only two names in the FC HBA area - Emulex and QLogic, they're both perfectly adequate but do ensure that you fit the card into the right slot - i.e. if it says it needs a PCIe x 8 slot then ensure that your slot is x8 or 16. Also make sure that the card you buy supports the exact operating system version you want to use, and pre-download/install the various device drivers and tools to your system before installing the card.
You can then cable it up to your array directly or via FC switches, for resilience try to use a dual-port FC HBA and run one cable to one FC switch and the other to a second FC switch - you'll probably need 50u OM3 or OM4 (for 16Gbps FC) multimode fibre, usually with LC connections at both ends.
If you're going via one or two FC switches then whoever manages them will need to 'zone' your new FC HBA ports to the array/s you wish to connect to. Almost certainly the only thing you'll need to do to help with this is let these people know the 'WWN' numbers of your FC HBA (one per port usually).
Your storage team will then be able to expose their storage LUNs to your machine BUT this isn't all you need to do - if there are other devices sharing the same LUN you need to match whatever they're using for their shared-file-system and locking methods. Again this isn't something you're likely to be able to help with but pretty much anything you want to do is possible, but may take a lot of re-work - either way speak with your storage team.
If you don't want to connect via FC then presumably you want to connect via ethernet/FC-over-Ethernet - in which case you need to buy a regular Ethernet HBA, connect its ports to your Ethernet switches and again contact your storage team to discuss how the shared storage is setup.
I hope this is of some use to you, it's not the simplest thing in the world to deal with but you'll get there eventually :)