There may be times when they, their, or them is an appropriate choice as a pronoun for a singular noun of nonspecific gender: most often after the use of nobody, everybody, one, anyone, or nouns that may be singular or plural, depending upon their usage: faculty or student body, for example. But when possible, rewrite the sentence.
The use of he/she or him/her, although more grammatically accurate in these cases, is often a distraction.
Anyone can take their medicine when it tastes like strawberry shortcake. (okay)
Anyone can take his or her medicine when it tastes like strawberry shortcake. (distracting)
Most people can take their medicine when it tastes like strawberry shortcake. (rewritten)
The faculty decided to take its resolution to the administration. (singular sense)
The faculty are very pleased with their new students this year. (plural sense, all members of the faculty)
We try to let each student take his or her exam home. (distracting)
We try to let students in this situation take their exams home. (rewritten)