can a immigrant become president of another country?

Based on article 54 of the Basic Law of Germany any German aged 40 years and above may be elected as Federal President. It is not a requirement to have acquired German nationality at birth or by being born in Germany. In theory an immigrant who has naturalized in Germany could become a candidate for presidency.

It probably depends on the country. In the USA for example, you must be born here to be president. And I will not respond to any racist comments about where Obama was born.

Depends on the Constitution & laws of the country involved.

Sam Houston was an immigrant to Texas before he became President of the Republic of Texas. He had previously been governor of a U.S. state (Tennessee).