Not a teacher.
Synonyms that can be used for "Sign in":
Sign in to TGA messenger! yes
Login to GTR messenger! yes
Enter the FTE messenger! not used in conversation
Do login in the FRE messenger! no, the repetition of "in" would sound weird to a native speaker
You might also say:
Get on/Get on to...
"Hey, I'll see you on AIM later."
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