"secure an internship" is a correct and usable expression in written English.
For example, you could use it in a sentence such as: "I am hoping to secure an internship at a local law firm this summer."
Her father is an art collector, and at least partly because of that, she's been able to secure an internship at Eli Klein Fine Art, a SoHo gallery.
While she did not find anything at the fair, she managed to secure an internship at an event-planning company she contacted before arriving in Beijing.
They coached him on interviews and then helped him secure an internship at UBS, which he then converted into a job offer.
Food stamps kept me from going hungry, and gave me the support necessary to eventually secure an internship at the Guardian.
By midway through that fifth year, Ingels had built up a portfolio of designs — including a car dealership, built underground — that was strong enough for him to secure an internship at OMA in Rotterdam.
Herein lies the game of chicken: if you wait for PE/VC recruiting in the spring and fail to secure an internship you could well end up having no summer internship at all.
I would argue that securing an internship is preferable to being unemployed.
Zulaimy wanted to go into the hotel business, and through her school, had secured an internship at the Marriott World Trade Hotel.
After finishing her law degree at the University of Northumbria, she decided to sign up with Standout Internships after having no luck securing an internship in the UK.
Case study: 'I secured an internship at Google' Media executive Alun Lucas, 37, decided against a specialist MBA as he wanted a broad range of skills to work across a multitude of industry sectors.
Since internships are often entry-level positions, if you're a graduate, you may want to check with your careers service at your university to see if they have any alumni or contacts to help you make introductions for securing an internship".
