You really should search a little before asking others for the information. It took 10 seconds to find the following link. I'm sure there are other links also.
This is subject to modification. Piles in groups can deviate quite a bit more, as long as the piles are not interfering with each other and the pile cap can perform properly.
Oftentimes the real issue is the eccentricity of reaction. If a pile is not plumb, it must be determined what is out, either the toe or the head. Is the pile a single or part of a group? The issue usually becomes a problem of statics.
I have always found plumbnss tolerances interesting.
a.) How do you check plumbness of say a 60 ft pile driven into the ground?
b.) what if the pile is plumb at the top and sweeps?
c.) How are the tolerancecs decided? Do they reflect the design capacity vs. design load?
d.) what happens if the pile is found out of plumb? How do you corrrect it and who pays?
Note that as innocent as these questions seem, they have sparked heated debates and firece arbtrations for a very long time.
Piles that are encased in a pile cap are very forgivng. The nominal +/- 3" can easily be extended to 15" for interior piles. The usual FS from the geotech giving net usable from ultimate is of an order of 3, thus a minor deviation from plumb will shrink the FS by the cosine of the deviation from vertical. Usually not even significant up to 10 degrees of lean, (2 inches in a foot). My specs have no deduction for out of plumb piles and require additional piles only for attempts that fail to achieve design depth.