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How would one add the agent noun suffix (normally -tor) to the verb 'plecto' (I weave/twist)? It's been a few years — about 10 — but if I recall correctly, verbs whose stem ends in 't' uses -sor as the agent suffix. This would be 'plectsor', which seems very unwieldy; however, plecttor is certainly not correct. Obviously in English there are verbs whose agent form is irregular, and some which have no such form. Is this the case with this Latin verb? If this is the case, what would be the correct way to form the noun in theory?
Thank you in advance.

You seem to be missing the four part in the verb's dictionary entry: plectō, plectere, plexī, plexus.
The agent noun is derived from the perfect participle stem, which for this verb is plex-.
This stem is obtained by removing -us from the participle listed in most dictionaries.

To this stem you add -or, so the noun you are after is plexor.
(This kind of counts as -sor because x=cs.)
The participle stem tends to be indicated by -t- or -s-.
One important aspect of using the perfect participle stem is that you have one less thing to memorize.

Good question! Let's break it down.

The root of this verb is plect- (notably not plēct- which has a different meaning!). If you look it up in a dictionary you'll see the four parts plectō, plectere, plexī, plexus, which literally mean "I weave, to weave, I wove, woven".

Now, the suffix is usually written as -tor, but a better way to think of it is -or, without the t. You put it on the supine stem, aka the past participle stem, aka the fourth principle part: this is the last form listed in the dictionary, the one that ends in -us. In this case, it's plexus. Take the -us off and add the -or and you're done, getting plex-or.

To go a bit more in depth, most verbs use a suffix -t- to make the fourth principle part, but some instead use -s-, especially third conjugation verbs ending in dental consonants. This verb happens to be one of those! The actual reasons for choosing one or the other are unclear, but seem to go back to Proto-Italic or even Proto-Italo-Celtic. Back then, either one could be used, but the speakers generally picked one and stuck with it by the time of Latin.

So that's where the s comes from, but why don't we see *plectsor? Well, that is indeed what you get when you glue all the pieces together. But the combination ts isn't allowed within Latin words (with the singular exception of etsi which is really two words written together for convenience). So the ts simplifies to s, giving plecsor. Compare the word for "night", in the nominative: noct-s → noc-s → nox.

Finally, cs in Latin is written as x, as in duc-s → dux. This doesn't actually change anything about the pronunciation, it's just a spelling quirk. So our final result is plexor.