No. Every cell in a timelord's body changes during regeneration. It is a very violent and often dangerous process to preserve the timelord's life. If you were to regenerate, not only would your face and body change, but also your personality. It's your body's last-ditch effort to save your life. Plus, it's implied that since a regeneration is so extreme on your body, it's possible for your body to fail and you die anyway.
In short, no, and it's not something you want to go through anyway.
However, Doctor Who is over 50 years old and plays fast and loose with its canon, so there have been some rare exceptions. Here are the ones that I know of:
The Second to Third Doctor regeneration stands out. In "The War Games," the Time Lords put the Doctor on trial and decide to exile him to Earth. They force him to regenerate, but they also allow him to choose his new appearance. This is the only time I can recall where a timelord is forced to regenerate.
In his first appearance in the new series, the Master was shot. His last words before regenerating were "If the Doctor can be young and strong, then so can I. The Master reborn!" He was able to go from an old man to young, energetic one. Interestingly, after regenerating, he was surprised at the sound of his new voice. This could indicate that Time Lords have some influence over their regenerations but not complete control.
The Romana incident. Unlike BIONICLE, where there is a clear canon, Doctor Who plays fast and loose with its own. There isn't an "official" canon; a 50 year old show is ripe with contradictions, so fans and writers are free to interpret "canon" however they like. However, sometimes a writer does something so stupid that everyone universally agrees that it never happened. Remember when I said that a regeneration is extreme on the body and is something you don't won't to go through? That it's the body's last-ditch effort to stay alive? Well, whoever wrote this didn't.