No, the Nintendo DSi does not come with a USB cable. When you open the box, you’ll find only the console itself, a stylus, the AC adapter for charging, and the usual documentation.
If you want to transfer photos, music, or homebrew files to a computer, you have two main options. You can buy a third‑party USB cable—often sold as a “DSi/3DS USB Cable” or “NDSL/DSi Charge & Sync Cable”—or you can use the DSi’s built‑in SD card slot to move files without any cable at all.