I'm glad to have come across her on Park Street this afternoon.

[sitifan]

I'm glad to have come across her on Park Street this afternoon. (by a Chinese teacher of English)
Is the above sentence acceptable?

 

[dunchee]

Yes.

 

[Tarheel]

It's not very natural. Perhaps:

I saw Mary at the mall. I was really glad to see her.

I guess by "acceptable" you mean would it be taken to be natural English. However, maybe you don't mean that. Maybe you want to know if people would understand what the person was trying to say.