If you mean "to influence or change":
* Impacting
* Influencing
* Changing
* Altering
* Modifying
If you mean "to produce a strong emotional effect":
* Moving
* Touching
* Poignant
* Emotive
* Heart-wrenching
* Compelling
If you mean "to feign or pretend":
* Assuming
* Putting on
* Acting
* Pretending
If you mean "to relate to or have an effect on":
* Concerning
* Relating to
* Pertaining to
* Involving
To choose the most appropriate synonym, consider the specific context in which you're using the word "affecting."