No. A sitting president can only be removed under the terms of Article II, Section 4 of the constitution, which reads, in its entirety:
The President, Vice President and all civil officers of the United States, shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high crimes and misdemeanors.
He is, of course, currently President Elect, and not a sitting president, but no one is likely to work up an indictment, try and convict him before January 20, 2017. Once he's in office, it takes impeachment (means indictment) to try him. The House has the sole power to impeach (Article One, Section 2). The Senate would then try the President (Article One, Section 3):
The Senate shall have the sole power to try all impeachments. When sitting for that purpose, they shall be on oath or affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no person shall be convicted without the concurrence of two thirds of the members present.
Judgment in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States: but the party convicted shall nevertheless be liable and subject to indictment, trial, judgment and punishment, according to law.
So you'd need the House to impeach him (it ain't gonna happen) and then you'd need the Senate to convict him, by a two-thirds vote (it ain't gonna happen), thereby removing him from office, before he could be prosecuted in the normal fashion.