Where is the job based? In many jurisdictions, negotiation which is not written into the contract but still formed a basis for your accepting the role can still be legally considered contractually binding. You might want to seek advice from a lawyer.

You can do lots of things, but what are you prepared to do? Quit? Complain?.... do you have a union?

is your boss also the one who promised the raise (or did he know about it?). if yes: leave. i no then there are still (legal) routes you can take

Promises only have the potential to be as good as the paper they are written on.

That's a good lesson learned: promises means nothing unless they are black and white on your signed contract.

I don't understand why this raise is so important? You moved abroad for the promise of a raise after 3 months, not for the job itself? Did you intend to quit after 3 months in some foreign country if you didn't get a raise? I get that you'd like them to keep their agreement, but people take jobs based on the entire job not the promise of a raise.

"what can I do for them to stay truth to their agreement?" - you could talk to your lawyer, but there's probably nothing you can do.

"we don't have the power to change that" must be the oldest trick in the book.

@user70848, what's probably going on is that the OP took a job that was barely able to pay their bills contingent on the idea they would get paid (much) better after those 3 months. Now the OP isn't getting that raise and is likely having to deal with money issues because of the move. Also, OP may have taken a less interesting job because it was going to pay better than another (more interesting) job after those first 3 month. A person will sacrifice some things to get more money to satisfy their creditors, but this time it's not working out, unfortunately.

Do you have any copies of the emails where they agreed to the raise? If not, can you get them?

The only thing the recruiter was interested in was his getting his fee when you were hired. He had probably forgotten what he just promised you within ten seconds of ending the phone call. Being a professional liar is just part of the job.

Is your right to be in this country dependent on employment by this employer?

@Harper, if it was a pay raise or a promotion otherwise and there was the agreement there was a pay raise in the future, then it's something many people would go for. The problem is still the employer reneging on the raise, not that the OP needs to "fix their budget". You assume a lot when you say people just need to change their budget to save money. There's a lot of people that simply can't pay just their required bills and food with their income, even with multiple jobs. I used to be one of them. Budgeting money only goes so far, then you need more money.

@Harper, how did you conclude the OP's lifestyle was an issue? Is it possible the OP needed that raise to be able to continue increasing their cash reserves and retirement funds?

“I’ve been… told… everybody in my department is very happy with me…” That is a standard management con. They see your integrity and personal sense of loyalty as something to exploit for profit, nothing more. I’m not saying every manager on earth does it, but in my experience it’s a common tactic.

Do you have an email in which they agreed to pay you the salary you wanted?

@Kat Yes, I do have all the emails in which we negotiated the contract, including the ones in which they agreed to give this raise.

@DJClayworth I have all the emails in which we negotiated the contract, including the discussion about the raise.

@Harper No, it isn't. I do not need a Visa to stay here.

@CramerTV Thank you for your comment ;-) That's my reality.

@delinear It's in Poland