Yes, a Vice President can run for President of the United States. In fact, there have been several instances in history where a sitting or former Vice President has successfully made the transition to the presidency.
The U.S. Constitution does not prohibit a Vice President from running for President. Instead, it allows any natural-born citizen who is at least 35 years old and has been a resident of the U.S. for at least 14 years to seek the office of the President. This means that individuals who have served as Vice President are entirely eligible to run for the highest office in the land.
Some notable examples include Joe Biden, who was Vice President under Barack Obama and later ran for and won the presidency in 2020. Similarly, George H.W. Bush served as Vice President to Ronald Reagan before being elected President in 1988. These cases illustrate that a Vice President can use their experience and visibility in office to bolster their candidacy for President.