Here's a LuaLaTeX-based solution. TeX-special characters, such as _ and &, may occur between pairs of backtick characters. Addendum to incorporate a follow-up comment by the OP: Care needs to be taken in order not to mis-interpret consecutive backtick characters -- those are generally used in TeX and LaTeX documents to initiate some instance of quoted material!

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{luacode}
\begin{luacode}
function backticks2tt ( s )
return ( s:gsub ( "`(..-)`" , "\\texttt{\\detokenize{%1}}" ) )
end
\end{luacode}
\AtBeginDocument{\directlua{luatexbase.add_to_callback(
"process_input_buffer", backticks2tt, "backticks2tt" )}}
\usepackage{url}
\begin{document}
aa `someFunction()` bb `some_other_Function()` cc
\end{document}
A comment on the type of pattern matching that's performed by the Lua function backticks2tt seems indicated. The pattern
`(..-)`
is the "non-greedy" way of specifying the pattern "all instances of one or more characters that are encased by backtick characters". To specify a "greedy" pattern match of "one or more characters" in Lua, one would type
`.+`
However, a greedy pattern match wouldn't be appropriate here, as it would end up grabbing the entire string
someFunction()` bb `some_other_Function()
in the MWE shown above and changing it to
\texttt{\detokenize someFunction()` bb `some_other_Function()}
Clearly, that's not right, and that's why it's necessary to specify non-greedy pattern matching.