I have it going the other way…my new monitor only came with a VGA cord (although the monitor itself has both types of video-in), my new computer only has DVI on the graphics card. Luckily, I had a VGA-to-DVI adapter in a drawer here and it works very well. If I weren’t using it, I’d send it to you!
Most DVI connectors provide VGA output (which is what the adapter does; it’s just a cable with a the two different connectors at each end).
If you have a full-size DVI connector, you should be able to see if it does or not provides VGA: Digital Visual Interface - Wikipedia - the only variant that you can’t use is DVI-D.
DVI-A, DVI-I and M1-DA are all ok.
The laptop’s specs or manual should also include this info.
ETA: oops, messed it up. I thought you wanted to connect the other way around. Still, the info should be valid if you read it the other way round