Canon: Not initially.
The Rebellion is made up of fugitives and disillusioned citizens of the Empire. These are people who either have no hope for a future (or survival) in an Imperial galaxy, or simply oppose the Empire's oppression. They are a wholly volunteer force: Any payment, if at all, is likely nominal and not the determinant of their allegiance. Whatever the case, the Alliance generally doesn't "hire" recruits.
However, we do know that payment is rendered for soldiers who complete their service to the Rebellion, at least after the war is over during the reign of the New Republic. When Poe Dameron's mother mustered out (discharged) after the end of the rebellion, she was given an A-Wing as part of her compensation package. This suggests that a payment scheme exists for Rebel soldiers, or that they are simply promised payment and reward if they survive long enough to get it (ie. the Empire is dead and the Rebellion is victorious).
Legends: Possibly, at least for some
At the Rebellion's inception, during the signing of the Corellian Treaty, the initial members are the planets of Alderaan, Corellia and Chandrila. Alderaan provides the funds, Corellia the fleet and Chandrila the troops. In this case, these are likely professional forces owned or raised by these systems, and therefore salaried. As far as I am aware, the Rebellion of Legends is a largely volunteer ragtag force, like in canon, but does maintain a small professional core as the elite, an element I'm not certain exists in canon.
Of course, beyond the basic fulltime forces, volunteer or otherwise, the Rebellion does employ mercenaries, informants, smugglers (like Han Solo) etc. who do jobs normal soldiers can't or because they are better positioned to do it. The Rebel leadership does pay up, so you could consider this as an example of the Rebellion paying for some of their labour.
We know that Han Solo was paid for rescuing Leia and the Death Star plans, but only because he's not yet a Rebel and he asked for payment, because he was expecting to be paid. Once he decided to hang around in the Rebellion, however, we all know he was eventually shipped off to Jabba for not paying back his loan. It could be a case of Jabba being fed up and not accepting repayment anymore, or it could be a case of Han returning his payment once he joined the Rebellion and then not being paid while serving.