Is it permissible to say: "I have submitted to Allah"?

The correct phrase is "I have submitted to Allah" (أسلمتُ لله) because the preposition "li" (لِ) is the appropriate one, and this is the usage found in the Holy Quran, as in His (the Almighty's) saying: "When his Lord said to him, 'Submit,' he said, 'I have submitted to the Lord of the worlds'" (Al-Baqarah: 131). As for making "aslama" (أسلم - to submit) transitive with the preposition "bi" (بِ), it is not known linguistically, but there is no sin upon whoever says it.