Yes, it is appropriate. That is one of the meanings of the word 'memory'. It's meaning #2 here:
memory - WordReference.com Dictionary of English
For example:
"Grandma's memory isn't too good any more. She used to have a really good memory when she was younger, but these days she often forgets things"
or
"I recognise you but can't remember your name. I have a great memory for faces but a terrible memory for names!"
Why the indefinite article? Because 'a [qualitative adjective] memory' describes a kind of attribute, like having "a great sense of humour", for example. We're all different when it comes to our ability to recall information: one person might have a good memory and another might have a bad memory.