Is it permissible for me to intend to give out one-tenth of the profits of a project for the sake of Allah, while saying: "Indeed, Allah is my partner in the project by one-tenth; He protects it and blesses our work"?

There is no harm in giving a tenth of the project's output as charity, as a means of drawing closer to Allah, seeking blessings through His obedience, and spending in His cause. As for the phrase: "Allah is my partner in the project with a tenth," its intent is legitimate, but its wording deviates from the transmitted expressions and contravenes the perfection of etiquette with Allah. Nevertheless, it can be interpreted in a correct sense, which is the commingling of what belongs to the questioner with what he has designated for Allah from the project's profits.