iTunes won't play .wma files as they are, but will convert .wma files to whichever format you've selected within your iTunes preferences.
In iTunes go Edit > Preferences > Advanced > Importing. There's a dropdown menu next to 'Import Using'...there you can choose which file type you want iTunes to convert the .wma files to.

If you want your songs in iTunes in .mp3 format, just download .mp3 files rather than .wma files
wma files aren't the most trustworthy anyway - check out this link:What you should know about WMA Files

The file will have lost some of it's data when it was originally converted to .wma format...if you convert that same file to .mp3 then it's going to lose more data during the conversion. So the quality of the file's going to be even more reduced.