Praise be to Allah.
It is better for the Muslim not to do that, and to err on the side of caution. The Prophet (peace and blessings of Allaah be upon him) said: “Leave that which makes you doubt for that which does not make you doubt.” Narrated by al-Tirmidhi, 2518; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
Based on this, a person should charge his mobile phone in the place where he is staying, before going to the Haram, so that he will have no need to use the electricity of the Haram.
But if a Muslim needs to do that, there is the hope that there will be no sin on him for that, in sha Allaah, if the people in charge of the Haram do not disallow that. But he should limit it just to what he needs and no more, so that he will not prevent any of his Muslim brothers from also charging their mobile phones, because they may need it just as he does, or more.
And Allaah knows best.