What do you think is correct? I've engaged in a new project or I've engaged on a new project
What do you think is correct?

I've engaged in a new project or I've engaged on a new project.

Is there any other way?

Thanks!

Question

What do you think is correct? I've engaged in a new project or I've engaged on a new project
What do you think is correct?

I've engaged in a new project or I've engaged on a new project.

Is there any other way?

Thanks!

Answer

"I'm engaged on a new project" - means you are doing work on the project.
'Working on' or 'working in', generally can be used interchangeably, but "I have engaged on a new project", somehow doesn't sound correct. 
"I have engaged in a new project", sounds like you started working in/on a project.

Answer

As Wardaa said, "I've engaged in a new project" is the better of the two options, but it isn't very natural.
"I've become engaged in a new project" would be better if you want to use 'engaged'.
"I've become involved in a new project" would be better still.

Answer

I believe the first sentence is correct: "I've engaged in a new project."

Here is why:
[engage in something] to take part in a particular activity, especially one that involves competing with other people or talking to them.
Here is an other option: " I've taken part in a project."

I hope this was helpful :)

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