First question would be if there's anything wrong with that finger like an old injury or something.  Are there any other activities you do, like touch-typing for example, that use it at all?  And does it work normally for you in those other activities?  Sorry if that may sound like a bunch of obvious questions, but it would be good if you are sure there isn't a medical cause for the difficulty.

If the finger is actually ok and all that, well it's not that unusual for the 4th finger to need some extra work for a lot of people.  From what I can tell, there are even books of violin exercises or etudes just for developing "finger independence".  It's not just violinists, either.  Guitarists, pianists, flautists, lots of musicians end up having to do some extra work to get the pinky to work for them. 

I also know an exercise that I learned many years ago that you can try.  Excuse the video quality though.  It was taken a few years back with a really crappy recorder.

Glad if it can help.  One pointer I'll give you is that keeping the hand relaxed makes that exercise easier to do.

Glad if anyone finds it useful.

I have found it a useful exercise for many instruments, and nice because it can be done when there isn't an instrument handy. 

Now for violin specifically, I use one sometimes that I got from a book by Leopold Auer, one of those "old masters". 

Put your first finger down on the E string at F.  Then without taking the first finger off, put your second finger down at C on the A string.  Then put down your third finger at G on the D string.  Then the 4th (pinky) finger down at D on the G string.  

Just getting all 4 fingers in those places at once is some "exercise" at first.  LOL

But after you get that, then you lift each finger and drop it on the note several times.  Then the next step is to do each one while plucking the string, so you can hear if you're getting a good note.  Then try it with the bow.  

Later, you can try playing those notes (with the fingers down and then trying lifting and dropping them, as above) but doing it in the order A string, G string, E string, D string, so you can practice skipping over strings with the bow while changing notes.

That whole routine will keep you busy for a while.  But it gives a lot of basic abilities a nice (I didn't say easy) little workout.  I have a little 5 minute routine I do with it.  But at first, just getting the fingers all down in those spots without muting other strings and etc is definitely enough to be education.  Add the steps after that one at a time as you get more comfortable with it.  Might take a few days or a couple weeks of trying it every day before you feel ready to move on to the next stage.   That is just fine, though.

Be gentle but persistent with yourself, and you'll get places.