My employer's HR manual (I just checked) specifies that we may use (paid) sick leave to care for sick (and/or the medical needs of, e.g. doctor's visits) immediate family members, which it defines as a child, parent, spouse, or same-sex partner. Assuming the state I live in keeps same-sex marriage legal, as it has recently been required to do, I'd guess that last category may eventually be removed; until very recently, there was no such thing as a same-sex spouse here, so the distinction has been necessary.
In short: yes. As others have noted, FMLA is an option if needed.