Wikipedia article on [Baire category theorem](https://en.wikipedia.org/wiki/Baire_category_theorem) and several other sources mention this paper: Blair, Charles E. *The Baire category theorem implies the principle of dependent choices.* Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 10, 933–934.
[MR0469765](https://mathscinet.ams.org/mathscinet-getitem?mr=0469765), [Zbl 0377.04011](https://zbmath.org/?q=an%3A0377.04011). However, I did not succeed in finding this paper online.

Still you can find this result for example in:

 * Horst Herrlich: *Axiom of Choice* as [Theorem 4.106](http://books.google.com/books?hl=en&id=JXIiGGmq4ZAC&pg=PA105)
 * [Theo Bühler](https://mathoverflow.net/users/11081/theo-buehler), Dietmar A. Salamon: *Functional Analysis* as [Exercise 1.7.14](https://books.google.sk/books?id=6lxoDwAAQBAJ&pg=PA48)
 * John C. Oxtoby: *Measure and Category*, notes to Chapter 9, [page 95](https://books.google.com/books?id=Va_aBwAAQBAJ&pg=PA95)
 * Following the suggestion in Asaf Karagila's answer, I have look also into the book Eric Schechter: *Handbook of Analysis and Its Foundations*. It contains this result in paragraph 20.16. (The result is stated for *pseudometric* spaces, but in the direction BCT $\Rightarrow$ DC, a metric spaces is used.)

<hr>

I will freely admit that I found some of the above results simply by trying to search for some suitable phrases in [Google Books](https://www.google.com/search?tbm=bks&q=baire+category+theorem+dependent+choice) and [Google Scholar](https://scholar.google.com/scholar?hl=en&q=baire+category+theorem+dependent+choice). Maybe you might find some further references in this way. 
It might be also worth checking the work which cite the Blair's paper, you can try them, e.g., in [Google Scholar](https://scholar.google.com/scholar?cites=10178393810659337528), [Zentralblatt](https://zbmath.org/?q=rf%3A0377.04011) or MathSciNet. (I do not have access to the latter.) Or simply check the [books which mention this paper](https://www.google.sk/search?tbm=bks&q=blair+%22baire+category+theorem%22).