She highlighted the danger of joining Europe’s Schengen area, which allows free movement of people within a number of EU countries.
Ms May’s comments came in a speech to the Scottish Conservative conference in Troon.
She said the Union has also helped tackle terrorism across the UK.
The home secretary questioned Scottish First Minister Alex Salmond’s pro-European policies, saying he must spell out which powers an independent Scotland would be handing to Brussels.
She told the conference: “It completely defeats the SNP argument that Scotland would fare better with more control over its affairs when they seek to hand over so many serious areas of government elsewhere.
“And people want to know – and they have the right to know – what handing over those powers will mean.
“Maybe even joining a single currency. In the UK, we maintain control over our borders.
“Joining Europe’s borderless Schengen area could open Scotland’s border up to mass immigration.
“In the UK, we have an opt-out on justice and home affairs matters – almost certainly Scotland would not have an opt-out.”
The Schengen Agreement, named after the Luxembourg town where it was signed, abolished internal borders, enabling passport-free movement between 25 European countries.
But the deal is now under review, after surges in illegal migration from Africa and Asia, via Italy and Greece in particular, in 2011.
The home secretary went on to say that policing in Scotland and the rest of the UK had a strong tradition of co-operation when it came to tackling issues like terrorism.
She said UK agencies had been quick to provide support in the wake of the Glasgow Airport attack, and would again be offering their services to ensure safety at the city’s Commonwealth Games, in 2014.
Ms May said: “Working together, we’re fighting the scourge of international terrorism.
“Working together, we’re busting the international drug barons that ruin our communities, rip families apart and ravage the lives of so many.
“Working together we can look to the future as a United Kingdom.”
source: BBC © 2012