She made the announcement at the Dorset Rape Crisis charity screening of the show's final episode in Bridport, Dorset, on Monday evening.
Hesmondhalgh said she was proud to have "given a voice" to rape victims in the eight-part crime serial.
The charity said it was "excited" she had agreed to take the position.
The storyline of the third and final series of Broadchurch, which is part-filmed in West Bay, centred on the rape of Trish Winterman - played by former Coronation Street actress Hesmondhalgh.
Among the relationships that develop in the show is Trish's work with her rape counsellor Beth Lattimer, portrayed by Jodie Whittaker.
Tracy Parsons, from Dorset Rape Crisis, which worked closely with Broadchurch's writer and producer, Chris Chibnall, said the programmes had shown there was support for people struggling with the legacy of rape.
"We are really excited that Julie has agreed to be our patron - it's huge for our trustees, staff and clients that someone who is so well known is coming onboard," she said.
Hesmondhalgh said: "I was very relieved that I had given a voice - in my own small way in this big project - to the people who have been through [rape]."
Of her new role as patron of Dorset Rape Crisis, she said: "I feel very proud to be part of increasing the profile of anybody who is doing this incredible, important, essential work."
She described rape as a "pressing" issue, adding: "We need to start having conversations at home with our families - with our daughters and our sons - about consent and about respect, and about healthy, sexual relationships."

The military hero who defeated Napoleon Bonaparte in 1815 stayed at the Kent castle regularly from 1829 until 1852.
Copying a watercolour made shortly after his death, English Heritage has recreated the carpet and wallpaper in the room when he died aged  83.
A pair of his original Wellington boots and his death mask are also on show.
The bed and armchair he used are also on display as part of the new exhibition at the castle, which opens on Friday.
Displays in other rooms explore the career of Field Marshal Arthur Wellesley and his "celebrity" status and state funeral, where more than 1.5m people lined the route.
Wellington's body lay in state at Walmer for two months while preparations for his funeral at St Paul's Cathedral were taking place.
"In 1852, the eyes of the world fell upon Walmer Castle as one of the most important figures of that century died within a small and modest room there," said senior curator Rowena Willard-Wright .
Walmer Castle, near Deal, was completed in 1540 as one of a chain of coastal artillery forts.
From 1708 it became the official residence of the Lord Warden of the Cinque Ports, a position occupied by Sir Winston Churchill and Queen Elizabeth the Queen Mother as well as the Duke of Wellington.
The Lord Warden is now a ceremonial post but the holder was originally in charge of five port towns on England's south east coast.
Broadchurch actress Julie Hesmondhalgh has become the patron of a rape crisis charity following her depiction of a rape victim in the ITV drama.
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The bedroom where the Duke of Wellington died at Walmer Castle has been recreated to mark the 200th anniversary of the Battle of Waterloo.