Writing is not the same as reading, but reading does help, especially if you set out to read with the express purpose to improve your writing.
What I often do -- I'm not a native speaker, so my English could use some improvement -- is read something like The Economist and underline those word uses and turns of phrase that sound good or express a concept very concisely, which, while I do recognize them, are not part of my active vocabulary.
If you do this, you can get more out of it by going over the underlined phrases again, perhaps copying them into a notebook, but it may not even be necessary; just reading well-written material and paying attention to what it is that makes it well written can improve your own writing.