Could the governor call a referendum?

Not on his own. No Texas governor can single-handedly put independence on the ballot. The referendum is created by a law passed through the Legislature, and the governor is one part of that process, not a shortcut around it. But the governor's role is real, and his support matters.

A referendum is created by law, not by decree

Texas is not an initiative-and-referendum state, and the governor is not a king. There is no executive order that conjures a statewide independence vote into existence. A referendum exists only when the Legislature passes a bill creating it. That bill follows the ordinary path: filed, heard in committee, debated, and passed by both chambers. The governor cannot skip those steps and cannot manufacture the vote by himself.

Where the governor does fit in

There are two routes through the Legislature, and the governor figures differently in each. The cleaner route for the referendum is an ordinary bill, which needs majorities in both chambers plus the lieutenant governor and the governor, ending with the governor's signature. On that path the governor is a decisive yes-or-no. The other route is a constitutional amendment, which the voters ratify directly and which does not require the governor's signature at all. Either way, the governor is a player in the process. He is not the whole process.

The governor can also use the bully pulpit

What a governor can do, short of any signature, is lead. He can throw the weight of the office behind the bill, call a special session that puts it on the agenda, and tell the people of Texas plainly that they deserve the right to decide their own future. A governor who championed the referendum would move it faster than almost anything else could. That is influence worth pursuing, and it is exactly why the movement works to put independence in front of every officeholder in the state.

Why it still comes back to the people

Notice that every road runs back to the same place. Whether the vehicle is a bill or an amendment, the decision is not finally the governor's. It is the people's, because Article 1, Section 2 of the Texas Constitution places the power to alter or reform the government with them. The governor can help open the door. Only Texans walk through it.

The bottom line

A governor cannot call the referendum alone, but he can help pass it, sign it, and champion it. The vote itself belongs to the people of Texas, and that is exactly where it should belong.