thesis is Ancient Greek for "setting (down), placing", and @user438 is completely correct that the connection is that someone "sets down" arguments and propositions. Other related indirect senses mentioned in the LSJ dictionary include "instituting games", "setting forth" in legal form, monetary deposits, a "general question" (as opposed to the hypothesis, lit. "under-placing", the "special case"), a "downbeat" in music, and a stop in punctuation.
The earliest attestation of the philosophical sense given in LSJ, "thesis, position, assumed and requiring proof" is in Plato's Republic, 335a:
Notice how thesis "placing" is led up to in this excerpt by repeated use of the related verb tithēmi "to put; (mediopassive) to take up a position"—both in the same sense of "taking up an intellectual position":
καὶ μάλα, ἔφη, οὕτω συμβαίνει. ἀλλὰ μεταθώμεθα: κινδυνεύομεν γὰρ οὐκ ὀρθῶς τὸν φίλον καὶ ἐχθρὸν θέσθαι.
“Most certainly,” he said, “it does work out so. But let us change our ground ["change position"]; for it looks as if we were wrong in the notion we took up about ["in positioning"] the friend and the enemy.”
πῶς θέμενοι, ὦ Πολέμαρχε;
“What notion ["how did we position"], Polemarchus?”
τὸν δοκοῦντα χρηστόν, τοῦτον φίλον εἶναι.
“That the man who seems to us good is the friend.”
νῦν δὲ πῶς, ἦν δ᾽ ἐγώ, μεταθώμεθα;
“And to what shall we change it now ["change position"]?” said I.
τὸν δοκοῦντά τε, ἦ δ᾽ ὅς, καὶ τὸν ὄντα χρηστὸν φίλον: καὶ περὶ τοῦ ἐχθροῦ δὲ ἡ αὐτὴ θέσις.
“That the man who both seems and is good is the friend, but that he who seems but is not really so seems but is not really the friend. And there will be the same assumption ["position, thesis"] about the enemy.”