If you own a colorchecker, you can use DNG profile editor, or X-rite's passport Lightroom plugin to create a custom camera profile for your camera. This works really well. I should however caution you about an issue I discovered with this. One of the problems is that neutrals are not kept neutral when you change to a different camera profile in Lightroom or ACR. An illustration is given below.
On the left is the result of first assigning my self-calibrated profile generated using the passport plugin (this is also true for other profiles) and then using the white balance dropper on the neutral patch on the card and on the right is the result of first setting the white balance and then assigning the exact same profile. As you can see on the right, my very neutral grey backdrop turns green and the girl's skin is rendered a little too yellow. The skin tone might not be too bad but the green backdrop is very distracting I think. On the left, the color is just fine, no tint to the backdrop and good skin tone. The difference is simply in the white balance chosen by the white balance dropper. The image on the right, Lightroom chose 5700K and -3 tint, while on the left, it chose 5450K and +12. Quite a difference for white balancing on the same patch! I tested with all the other camera profiles and they all show this problem that there is a shift in the color temperature taken from the neutral patches.
P.S. if you prefer slightly more warm skintones than the very neutral rendering you get when using the neutral patch, the passport has a set of warming patches in the top row. You can simply select patches more to the right of the standard patch to warm up skintones. This results in the backdrop staying far more neutral but just the skintones warming up. A far more pleasant effect. See below for the result of choosing the patch two spots to the right of the neutral patch (the middle one in the top row of neutral patches. The second row of neutral patches also allows you to go to cooler colors and is more useful for landscape photography.
This made Lightroom choose 6000K and +27 tint. The skintone that resulted is very nice I think.
Conclusion: do your custom white balance after assigning the profile you want to use.
EDIT: It appears that this is mostly a problem with self-created dual illuminant profiles. I create these by shooting one image under tungsten light and another in sunlight as I don't own a calibrated D65 reference. Whether I create the profile in X-rite's passport program or DNG PE, they show the issue of neutrals not staying neutral. The Adobe-supplied camera-matching profiles also have the problem, but it is too minor to worry about. The differences in grey-card set white balance are on the order of 100K which you won't really notice.