When Sam first arrives at the Citadel he is greeted by an acolyte named Lorcas. Sam is told to sit and wait for the Seneschal. Sam expects this to a be short wait, but after a few hours inquires again and is told to wait. At this time Sam is approached by another acolyte, Alleras, who informs Sam that he must bribe Lorcas with a penny.
"A penny will serve. For a silver stag Lorcas will carry you up to Seneschal on his back. He has been fifty years an acolyte. He hates novices, particularly novices of noble birth." Alleras to Samwell Tarly, A Feast for Crows, Chapter 45
Alleras specifically says "of noble birth". To me this would imply that novices are accepted from any descent, noble or common.
Even the founding of the Citadel is a bit of a mystery to modern Maesters. From The World of Ice & Fire we find this excerpt in the "Oldtown" chapter.
The origins of the Citadel are almost as mysterious as those of the Hightower itself. Most credit its founding to the second son of Uthor of the High Tower, Prince Peremore the Twisted. A sickly boy, born with a withered arm and twisted back, Peremore was bedridden for much of his short life but had an insatiable curiosity about the world beyond his window, so he turned to wise men, teachers, priests, healers, and singers, along with a certain number of wizards, alchemists, and sorcerers. It is said the prince had no greater pleasure in life than listening to these scholars argue with one another. When Peremore died, his brother King Urrigon bequeathed a large tract of land beside the Honeywine to "Peremore's pets," that they might establish themselves and continue teaching, learning, and questing after truth. And so they did.
It seems what were the original Maester, even though not that by name yet, were from all walks of life and from all different places. Which seems to be confirmed a few paragraphs later:
Thousands of years before the first sept opened its doors, the city had been home to the Citadel, where boys and young men from all over Westeros came to study, learn, and forge their chains as maesters. No greater seat of knowledge exists anywhere in the world.
While this does not explicting state whether the recruits are noble or common, I believe there is enough context to sumize that they were from both common and noble houses.
This also implies that the Citadel may not have had to do much "recruiting". It seems the Citadel was famous and respected enough that students would willingly seek out and come to join the order.