Question: I'm trying to follow some of the best practices of the "open science" movement. In my thesis, I've performed all of the analyses in R (a non-proprietary, open-source program for analyzing data), and my datasets are in the non-proprietary CSV format. 

I would like to be as transparent as possible, by sharing my datasets and R analysis/code files with my thesis committee, and ultimately with the public once my thesis is finalized and placed in a repository. How can I best do this?

I was thinking about uploading my files to the Open Science Framework (<http://osf.io>) and citing them with a regular HTTPS link. Once my thesis is finalized, I would then "freeze" them on the OSF website (as I understand, this would prevent post-hoc changes), then get a DOI that points to the frozen files and cite that.

Are there any better options?

Answer: 
First, best compliments for your intent on open and reproducible research! 

Your code and datasets ought to bring you better visibility for your research. GitHub is a good alternative to publish your code. If your datasets involve elements of machine learning you may donate it to the UCI Machine Learning Repository.
I understand that this question is old but allow me to share my opinion. The OSF is one of the stable open data repository, just like Figshare, Zenodo, and many other similar free services. Many scientists have used it and I heard no complaints so far regarding its link or DOI stability over time. So it is very good for students or any scientist to post their dataset and code separately in this repository. 

I know that you can also do it the old way by embedding the code and data directly in the document (paper or thesis), but by making them available separately is highly advised to increase the visibility of your work. Other scientist can cite it just like they cite other scientific document, by adding the link and the DOI.

You can always contact OSF team to seek for advise on how to maximise your OSF account or how to cite documents on OSF properly. 

Just do it again for your future research, considering you must be graduated by now. 

Best wishes.