According to various interviews and featurettes, the idea was for the series to be timeless. However, certain dialogue and flashbacks inadvertedly place the series on a timeline. For example, in "The Blind Fortune Teller," a conversation between James Gordon and circus performers reveals that the series takes place at least a few generations after World War I.
In "Scarification," there are flashbacks to an earlier century (probably the nineteenth century) where it shows the founding families of Gotham City.
In "Spirit of the Goat," it is revealed that Harvey Bullock was active as a rookie cop 10 years before the start of the series, as was the serial killer known as the Goat.
With this evidence, I'd say that the series could take place anywhere from the 1960s to present day. Regardless, the series is set in a heightened reality. So no matter when it's set, the timeline and technology on the series is very different than ours.