How do I teach my cat to let me pet her?

About 6 weeks ago, I rescued a 2YO cat from a shelter. It turns out she had been in a cage in the shelter for 18 months (!). Over the last 6 weeks, she’s adapted to having the run of a house. She seems generally pretty happy. When I’m home, she’s near me and purring. When I’m not home, she spends a lot of time looking out the windows, basking in sun rays, and doing the things cats do.

But she won’t let me touch her.

She’s really interested in me, but she stops at a certain distance. If I squat down like a catcher, she’ll pace back and forth like she wants to come up to me, but doesn’t. If I’m on my bed, she paces around the bed and eventually sits down on the floor near it, but never on it. I’ve tried to gently coax her, but that’s been futile.

When I quietly reach out my hand to let her sniff, she runs away. If I try and pet her when she’s within arm’s reach, she runs away. The few time I have managed to gently pet her, she looked at me as if to say, “Um, what are you doing? Why are you touching me? I dont get it” and quickly ran away. I got the feeling, based on her history and her reaction, that she had never been petted before, and didn’t realize she was supposed to enjoy it (and eventually, because she’s a cat, demand it, on her own terms).

The easy answer is to get another cat (who is more socialized) and that cat will lead the way. But that doesn’t work for me, and I think my cat likes having a quiet home to herself.

Any ideas on how I can teach my kitty to like being touched?

Thanks!