Introducing a full agile framework can be daunting and cumbersome. Instead, try beginning with the method's core focus: continuous improvement. Retrospectives are the starting point of your agile journey and can help you solve the most immediate problems in your process, leading you down the road of process improvement.
If you asked anyone in my team what agile practice is most responsible for our success over the past eight years, I bet they'd answer "retrospectives". At the start of every two-week sprint, we spend time talking about the previous sprint, identifying areas that need improvement, and thiinking of ways to overcome obstacles. But I wonder if it's not so much the retrospectives themselves, as the small experiments (to borrow Linda Rising's term) we try to address our problem areas.