Republican Greg Abbott said he had allocated $1bn (£706m) in state funds to uphold border security.
“While securing the border is the federal government’s responsibility, Texas will not sit idly by as this crisis grows,” Mr Abbott said.
One of President Joe Biden’s first acts in office was to end border wall construction.
In February, the Democrat rolled back the emergency order used to fund his predecessor Donald Trump’s Mexico border wall – a key symbol of the former president’s agenda – and said no further tax dollars would be spent on it.
It’s not clear if Mr Abbott has the authority to order a wall in Texas independently.
“It will help all of us to work on ways to stem the flow of unlawful immigration and to stem the flow of illegal contraband,” the governor told a press conference on Thursday.
But the plan is likely to face legal challenges.
The American Civil Liberties Union of Texas called it “an attempt to distract from his governing failures while targeting vulnerable immigrants”.
Migrant surge hits 20-year high
This month, the number of undocumented immigrants reaching the US-Mexico border hit its highest level in more than 20 years.
US Customs and Border Protection said it had apprehended 180,034 migrants, mostly single adults, in May – the highest monthly total since April 2000. The majority are fleeing poverty and violence in Central American countries like Guatemala.
A pandemic emergency rule known as Title 42 allows border agents to turn away most single adults and many families.
However, it does not apply to unaccompanied children. Thousands have crossed the border and are being held in US immigration detention facilities.
Tensions have been mounting between the Biden administration and Mr Abbott, whose state is an epicentre of illegal crossings.
Justice Department officials threatened to sue Texas after the governor ordered child-care regulators to cancel the licences of centres that shelter immigrant children.
On Thursday, Mr Abbott blamed the rise in migrant crossings on Mr Biden’s policies, saying he hoped to give more details about the wall next week.
“Some of these border barriers will be built immediately,” he added.
A Trump legacy
Building a southern border wall was a signature pledge of Mr Trump’s 2016 presidential campaign. He initially insisted Mexico would pay for the wall – which it declined to do. By the time Mr Trump left office, the US had spent about $15bn (£11bn) on the project.
According to the New York Times, the Trump administration built more than 450 miles of new wall, most of it in areas which had older barriers already. Much of this was in Arizona rather than Texas, where some landowners took legal action to resist construction on their properties.
Mr Biden promised a more humane immigration agenda, declaring in a presidential debate that the separation of children from their parents under the Trump administration’s zero-tolerance policy was “criminal”.
He has launched a task force to reunite separated migrant families, and repealed Mr Trump’s “Remain in Mexico” policy, which required US asylum seekers to wait in Mexico while their applications were processed.
Republicans have blamed Mr Biden’s policies for the border surge, however – as has Guatemala’s President Alejandro Giammattei.
Before meeting US Vice-President Kamala Harris this week, he told CBS News that after Mr Biden took office, “the very next day the coyotes were here organising groups of children to take them to the United States”.
During her visit, designed to address the root causes of immigration, Ms Harris told illegal immigrants thinking of making the trek to America: “Do not come.”