There has been to date no indication of this. On the contrary, she outright states in "The Time of the Doctor" that she fancies the Doctor and this is a plot point in "Deep Breath", where she even appears offended at perceived interest being shown in her by Madame Vastra. One of Clara's splinters, a woman in the future called Oswin Oswald, claimed to have fancied a girl once, but dismissed it as "going through a phase" ("Asylum of the Daleks"). The minisode "Clara and the TARDIS" has a moment where two Claras (the same Clara from different times) talk about sharing a bed, however this was in a situation where Clara's bedroom had been lost and so the bed sharing was suggested as a necessity to allow both versions of Clara to get a good night's sleep rather than for any sexual reasons. Also, she dates Danny Pink in "Listen".
However, in Series Nine, there have been subtle references to Clara's sexuality, and it appears she may be bisexual. In "The Magician's Apprentice", she advised her students that Jane Austen was a "phenomenal kisser", and in "The Girl Who Died", Clara tells the Doctor "I'll fight you for her" making it sound like she's attracted to Ashildr. Later, in "Face the Raven" she talked fondly of playing pranks with Austen, telling Rigsy, "I love her ... take that how you like" which still leaves the matter ambiguous.
So, to sum up, she is definitely not gay, but she may be bisexual.