Here's how: If you review a paper for a major sociology journal that you think deserves to be published (or to be published after adequate revision), you could copy and paste this at the end of the COMMENTS FOR AUTHOR section of your review:
I think the results of this paper are sufficiently interesting and provocative that I can imagine the possibility of others wanting to verify the results or to build off these results in future work. For this reason, I strongly encourage the author to deposit code and other information relevant for reproducing the results in an permanent online archive at the time of publication, and perhaps even indicating that this has been done in a footnote to the paper (e.g., "Code used in the analyses presented in this paper is available in the ICPSR Publications Related archive"). Such archiving at the time of publication is becoming standard in economics, and I see no reason why this work is less important or less worthy of serious anticipatory attention to replication than what economists do.Okay, you might think the last sentence is a little much. But, that aside, there is presumably nothing insincere in your saying at least the rest of this. In other words, presumably in thinking that the article should be published in a major sociology journal you do think the article is worthwhile enough that someone could care about whether its results can be verified or care otherwise about the decisions the analyst made. If you don't think this about the paper, why do you think it deserves prime sociology journal space?*
And in the COMMENTS FOR EDITOR section, copy and paste this:
See paragraph at the end about code and/or data sharing. I urge you to underscore this point in your letter.As Margaret Mead once said, "Never doubt that a small group of thoughtful, persistent reviewers can change the prevailing methodological practices of a discipline. Indeed, it is the only thing that ever has."
* I mean, if your opinion about the worthwhileness of sociological research is so low that you would recommend publication in a major journal of findings that you can't imagine anyone actually caring much about, why are you in sociology? Unless you are old and stuck and can't do anything else, but, if you are that alienated/disillusioned/disenchanted, why are you still reviewing papers? Seriously, life is too short, do something else with yours.