Cirstea, who plans to retire later this year, has already delivered the shock of the tournament by stunning world number one Aryna Sabalenka in Saturday's third round.
She now stands just one win away from breaking into the top 20 for the first time in her career, having previously reached a career-high ranking of 21 in August 2013.
"I always said there's no expiration date for ambition and dreams," said Cirstea, the 26th seed in Rome.
"I think everyone can see that I absolutely love this sport. I have so much passion for it. For me to play here and be in the semi-finals in Rome is absolutely amazing.
"I'm so grateful to the sport. I'm just really, really enjoying my week in Rome so far."
Cirstea's remarkable clay-court form has seen her suffer only two defeats this season on the surface - against two-times major winner Coco Gauff at the Madrid Open and Russian teenager Mirra Andreeva at the Linz Open. She was also forced to withdraw from the Open de Rouen semi-finals due to a leg injury.
Fittingly, she will face one of those two players in the last four in Rome.