I know we can say, "Call it a day" at the end of a day. Can I say, "Call it a project" meaning successful completed project?
You could say that, and in context it would probably make sense to those involved, but it isn't exactly a common idiom.
Maybe you'd prefer "That's a wrap!"
Edit for more details:
If I was working with someone on a group project and they said "Let's call it a project!" I would understand it as "We are finished working on this, it is as finished as it is going to get" or "good enough" (Similar to "Let's call it a day", although if you call it a day you are saying you are done working that day, and presumably will come back the next day to do more)
"That's a wrap" has the same general feel of you are finished working on it, although "That's a wrap" doesn't have the same "good enough" implication. It is more like "this is a good finished project". As a commenter pointed out, this has come from the film industry when they would finish shooting.
Both "that's a wrap" and "call it a day/project" are very casual sounding, so I would say them to partners, but not to superiors or in formal writing.
In response to some of the comments, here are some other options:
"I think we have ourselves a project!" - expresses completeness and excitement
"Let's stick a fork in it and call it done." - Another "good enough" sentiment
"Ship it!" - Could be either "good enough to sell" or actually complete/finished, depending on context.
"Call it a day" does not mean "successful completed day"... it means "it's time to leave, let's stop for the night".
There's no implication that the day was particularly fruitful... in fact, it's often used in cases where the day wasn't particularly successful.
You've been hitting your head against that wall for the last 10 hours and staying here isn't going to make it any better. Call it a day, go home, and come back fresh tomorrow.
So there would be no equivalency between "this project is now successfully completed" and "call it a project" because there is none in the "call it a day" idiom to start with.
If anything, you risk it sounding like you're saying the project outcome is mediocre rather than completely successful:
Well, this is the best we can do with this project, so let's call it done and ship it out.
No, the idiomatic phrase call it a day is never modified in that way. We do have some variations, including call it a night, but they typically refer to the time period when work was being done and not the thing being worked on.
Call it a project may or may not be understandable to native speakers depending on the precise context, but it will almost certainly sound awkward. We do sometimes play on idioms by replacing one or two words like this (often for humorous effect, sometimes intentionally being ungrammatical), but that can be hard even for native speakers to pull off successfully.
"That's a project" is often used in the sense of something being a big undertaking. With that context, using "Call it a project" may give a sense of work lying ahead rather than work being wrapped up/temporary halted as implied by "Call it a day."
Can I say "Call it a project" meaning successful completed project?
You can say it, but to be better understood by a native English speaker you might instead say,
"We have successfully completed the project!"
As other answers have pointed out, "Call it a day," implies some measure of cutting your losses, or maybe a tactical decision to get some rest and get back to work tomorrow.
If that's the feeling you're going for with, "Call it a project," may I suggest:
It's often used in software or product development to mean, "This is as good as it's going to get without significant extra effort. We can't justify the additional cost (time, money, manpower), it's good enough"
I've never heard anyone say that - maybe I'm just lucky. It just sounds like contrived business-speak to me: poor use of language. Why not just say "well done everyone, that's a successfully completed project"?
To me, "Call it a project" would mean, "You know, this isn't just messing around any more. This has gotten big, and serious: let's call it a project!"
If we'd finally gotten something (mostly) done, I'd say "Let's call it done" or "That's a wrap".
If you just said "call it a project" out of the blue, I think I'd be confused; I'd have to think about it a bit before I'd start to figure out you might be inventing a variation on "call it a day".