She also distanced herself from past comments supporting the death penalty.
Ms Patel was appointed home secretary in July, when Boris Johnson became prime minister and overhauled the cabinet.
Her interview comes after she and Mr Johnson announced last week the recruitment of 20,000 more police officers in England and Wales.
These extra officers will replace the 21,732 police officers lost since 2010, when the Conservatives came to power.
Ms Patel told the Mail: "I've always felt the Conservative Party is the party of the police and police officers.
"Quite frankly, with more police officers out there and greater police presence, I want [criminals] to literally feel terror at the thought of committing offences."
She added: "My focus now is restating our commitment to law and order and restating our commitment to the people on the front line, the police.
"The key thing is that we empower them to stop criminality."
Asked about her views on capital punishment - after she previously made comments in support of it - Ms Patel said: "I have never said I'm an active supporter of it and (what I said) is constantly taken out of context."
In 2011, Ms Patel spoke about the death penalty on the BBC's Question Time, where she said: "I do actually think when we have a criminal justice system that continuously fails in this country and where we have seen murderers, rapists and people who have committed the most abhorrent crimes in society, go into prison and then are released from prison to go out into the community to then re-offend and do the types of crime they have committed again and again.
"I think that's appalling. And actually on that basis alone I would actually support the reintroduction of capital punishment to serve as a deterrent."