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.)
 * Some versions of Baire Category theorem are listed (together with references)  Paul Howard, Jean E. Rubin: *Consequences of the Axiom of Choice* under [Form 43](https://books.google.com/books?id=ffXxBwAAQBAJ&pg=PA31).

EDIT: Some sources mention that the result was proved again later in this paper: <cite authors="Goldblatt, Robert">_Goldblatt, Robert_, [**On the role of the Baire category theorem and dependent choice in the foundations of logic**](http://dx.doi.org/10.2307/2274230), J. Symb. Log. 50, 412-422 (1985). [ZBL0567.03023](https://zbmath.org/?q=an:0567.03023), [MR793122](https://mathscinet.ams.org/mathscinet-getitem?mr=793122).</cite><hr>
(G. H. Moore uses this [in the introduction](https://books.google.com/books?id=3RLGKcEjVIoC&pg=PR8) of his book *Zermelo's Axiom of Choice: Its Origins, Development, and Influence* as an illustration that some kind of database with consequences of AC might be useful to decrease likelihood of reproving already known results.)

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 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](https://mathscinet.ams.org/mathscinet/search/publications.html?refcit=469765&loc=refcit). (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).