My rickenbacker 4003s neck looks it turns to the right towards the headstock, is this normal?

I can't figure out what you mean.

A pic would be very helpful. Is the neck not flat/straight, front to back? Or is it actually warped sideways?

 

Realize that the nut is "taller" on the E string side and that may be throwing off your perspective.

 

Love the gray blanket.

 

I don't think I see anything that doesn't look like a Rick.

 

From these pics, nothing strange can be seen.

 

You need to post a picture looking down the neck from the head stock with the frets pointing up. That's the only way I'd be able to detect a twist like you seem to be worried about, but even then, it would have to be somewhat severe to see it in a picture. In the end, if it play fine, I wouldn't worry about.

 

I’d pick up the bass, and sight down it like in my photo, then you would get a sense of how flat the neck is, and whether it twists from side to side.

 

Looks like you have a little bit of a rise in the fingerboard right there at the nut. If that's what you're referring to, it's not a problem on a fretted bass and I wouldn't worry about it.

You also have some visible relief ("bow") in the neck,probably more than you really need. This can be adjusted out with the truss rod system (get someone to show you how to adjust this on a Rick).

A twist in the neck would be a different problem....

L

 

Looks good. I'd like to know what the neck measurements are.... looks nice and thin to me. Perhaps it's the photo angle. Is that a fireglo?
Sorry, I'm not helping answer your question... just lusting over a red 4003S.

 

On a different note-I’d also advise to have someone (I do it myself, not hard) slot your nut with nut files. I can see you have the high factory nut, which has the strings coming out of the nut much higher than ideal, you have to press a long way before you hit fret. In an ideal set up, the nut slot (where the string sits and comes out of the nut) is just a touch higher than the fret, and pressing down to fret a note is no further than going from fretted note to fretted note- to test this, watch how far the string has to travel down to the fret at the first fret, then, compare that to the distance that the string travels to the second fret when you are holding down the string at the first fret- they should almost be the same, maybe having a little extra height at the nut. Here is a photo of my Ric nut for comparison. Slotting the nut makes the action at the low position much nicer, FYI . I mention this because of your photo, and noticed the sky high nut that has come with my Rics

 

And mom says you can't your Ric until you clean your room.

 

If the above is true, it shouldn’t matter, but I don’t think any part of the neck should be “curved”unless it’s the back of the neck

 

I do believe you are seeing things not there.

Play it and stop worrying

 

Having owned a 1976 4001 from 1981 until 1992, then a 4002 (yes, "2," not "1" or "3") from then on, and at one point my main gigging bass with no backup, I concur that it is probably a combination of an optical illusion of the nut slots and a little too much relief. The RIC owners manual says to adjust the neck dead straight. Yes, that works. Personally, I like to "dig in" occasionally a little more than the average player, so with the double truss rod system, I adjust the G string side dead straight and the E string side with just the slightest bit of relief to give the E string a little more excursion room without fret slap. And this is with the old-style "hairpin" truss rods, which have never caused a bit of trouble to me. The "new" truss rods as on the OP's bass are simple to adjust by comparison.