Modestly. The supposed idea of IQ is that it is a measure of inherent ability. In practice, it is not, but it is still primarily a measure of inherent ability, so while a person can change IQ by training (doing things that exercise the brain), the variation is a secondary effect. You would not truly change your "intelligence" but you would change your ability to employ that intelligence.
It is sort of like running. You can train and improve your run times, but the individual has a basic structural (in-borne) limit, and fast people will mostly still be fast even if they can get a bit faster, and slow people will mostly be slow even if they can get faster; they will never really ever become as fast as the naturally fast people. But they can still get better than they were to begin with.