So I have been trying to make moves on this girl, I have been texting her all day and she never mentioned she had a boyfriend throughout the whole conversation. She was very happy to hear from me and carried on the conversation. But when I asked her out on a date to get ice cream sometime this week she replied: "I am kind of seeing someone right now but it is not official, I don't think he would like it if we went out together."
How should I handle this situation? I don't think her feelings are that strong for him considering the way she was talking to me all day.

Is it safe to still talk to her once in awhile?

She sees you as a potential friend. By her declaring that she's seeing someone it's quite evident she's establishing that frame. Be respectful and accept what she's telling you w/o reading into it.

She likes you as a friend only, and is trying to make it clear to you in a polite way that she's not romantically interested.

The other guy may or may not exist, don't read into it, this is just a girl nicely turning you down.

Respect her wishes, NEXT romantically. If you actually want to be her friend, go for it. If not, NEXT entirely.

On to the NEXT one.

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^^ This exactly. Well put.

she said no for the date. you simply move on and try to talk to other potential dates. keep her as a friend and never try to seduce her, with time she might be intrigued. you know the rest. thats the best chance youve got.