How to surround code by curly braces in IntelliJ IDEA?

Yes, try Ctrl+Alt+T (Surround With), then A (Curly Braces).

Just configure Smart Keys as follow:
IDE Settings > Editor > General > Smart Keys > Surround selection on typing quote or brace.

From the IntelliJ built-in help:

If this check box is selected, the selected text on typing a quote, double-quote or brace, will be surrounded with these characters.

If this check box is not selected, then the typed quotes, double-quotes or braces will replace the selection.