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This question is more related to the academical application of Physics than to Physics per se. I'm currently doing my thesis, and it involves a lot of molar masses in the calculations. I would like to know from which reference should I extract the molar masses of the different chemical elements. I'm currently extracting the values from Wikipedia or simply by Google search, but that seems to me a bad procedure. I solved the problem for the case of the physical constants extraction: I now use the CODATA ones. Is there any succinct paper for the molar masses like the CODATA one is for the physical constants?

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I believe that the chemistry equivalent of CODATA is the Commission on Isotopic Abundances and Weights (CIAAW). They have a website with the most current data, and they regularly publish reports on the latest measurements of atomic mass data.

As of this writing, the most recent published report is

J. Meija et al., Atomic weights of the elements 2013. Pure Appl. Chem. 88, 265-291 (2016).

In addition, the following bulletins have revised a few of these masses since the most recent scholarly article:

"Standard Atomic Weight of Ytterbium Revised", Chemistry International, Volume 37, Issue 5-6, Pages 26–26 (October 2015)

"Standard Atomic Weights of 14 Chemical Elements Revised", Chemistry International, Volume 40, Issue 4, Pages 23–24 (October 2018).

There is also a handy table on the CIAWW website which compiles all of this data.

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