It is possible, and the mother-son relationship is one of the stronger arguments you can bring to a warden's office. Wardens do grant waivers in situations like this, and family visitation, particularly from a parent, is something many administrators are willing to accommodate when the circumstances are reasonable.
The nature of the pending charge is the biggest variable. A minor charge that poses no obvious threat to facility security or the inmate's wellbeing is going to be received very differently than something serious or violent. Going into the request with a clear understanding of how your charge will be perceived and being prepared to address it honestly is important.
The approach matters as much as the facts. Wardens respond to humility and respect. A written request that is polite, straightforward, and acknowledges the unusual circumstances without making demands or excuses gives you the best chance of a favorable response. Explain who you are, your relationship to your son, why the visit matters, and why you believe granting it is appropriate despite the pending matter. Keep the tone cooperative throughout.
A pending charge is not a conviction. That distinction is worth making clearly in your request. You have not been found guilty of anything, and treating you as though you have before any legal determination has been made is a position the warden has discretion to push back against.
Be patient with the process. These requests do not get resolved overnight, and following up respectfully if you do not hear back within a reasonable window is appropriate.