Can I use a Triac dimmer circuit to control the brightness of an AC powered LED light strip?
Certain types of LED light strings will work with AC Phase Control dimming - but most will not work.

What will most likely work is the series strings of LED Christmas Lights.  These are simple series strings of LEDs with sufficient series resistance to keep the current at the proper level when fed with the rated AC voltage.  The strings of this type that I have seen are actually two strings connected in inverse-parallel - one string conducts on one AC half-cycle, the remaining string conducts on the other AC half-cycle.

However, most LED lighting uses some form of Switch Mode power supply.  Unless the power supply is specifically designed to work with AC Phase Control dimming, they most often do NOT work properly.

Like the comments say - how well this will work is completely dependant on how the LED string is designed and constructed.

Take one apart and see how it is built.  Add your findings to your question and we can offer an opinion as to how well it might or might not work.