If anyone steals from my property, do I have the right to steal something of his?
No person has the right to commit a public offence in retaliation. Theft is a public offence, and a person who commits theft can only be punished by the State authorities. As the aggrieved party, you must bring the matter to the relevant state forum and let justice take its own course.
Neither Islam nor any civilized state allows people to take the law in their own hands; the simple reason is that if this right is given to people themselves, no one can check whether justice has been truly carried out or not. Such a right would be tantamount to jungle law, and would therefore only give rise to anarchy.