ou CAN. Sort of. I have not played in awhile, so I don't remember the name of the action but you are able to click a button with the fleet selected that orders your fleet to defend a certain area, such as system, sector, anywhere. The fleet will respond to attacks within the area that it is assigned. Just make sure that the AI does not have any control over your fleets, it will override your home systems and your fleet orders.
What you refer to is the defensive posture, but postures require the fleet(s) to be automated in order to work (fleet formation in empire policies, however, absolutely should not be automated if you want postures to work properly). Gelatinous Cube's thread How to Fleet Posture (check the Guide to Guides for a link) should get Balkor Wolf started if he or she needs a refresher or doesn't know how to set fleet postures up.
There is one other way that you can set up a patrol route of sorts. If you hold down the control button and right click on an object, such as a system, you should get an action menu for whatever you have selected. One of the actions is "queue next mission." If you want to set up a patrol route that covers multiple systems, you could queue multiple move orders for the fleet. However, I don't know how many orders you can add to the queue, and you cannot make the queue loop, so this could easily become something which requires too much management to be worthwhile, practical, or enjoyable, especially if managing large numbers of fleets.