I'd like to add a small icon on my blog similar to the other social networking icons available that links to my careers CV. Is there an easy place to download a copy of the bar graph careers logo and am I allowed to use it to link to my CV on my site? If the icon isn't readily available for download, am I allowed to crop out the piece I want from the banner on the careers home page?
Yes there is, you can find all Stack Exchange logos in the Logos and Icons page. You should thoroughly read and follow the Guidelines for the Use of the Stack Exchange Trademarks, and although the exact use case you have in mind doesn't seem to be covered I'm guessing the paragraphs on "Use of Our Name or Logo in Advertising" and "Promoting your own Account" apply (IANAL).