Disclaimer: The real answer to this question is does this symbol exist somewhere in a math font. That I do not know. But, just as a proof of concept, you could create the symbol using TikZ. Whether this is a good idea and how this fits with your math font of choice is another matter.
I've called the symbol \SDelta and it is scaled using scalerel to match the size of \Delta.

\documentclass{article}
\usepackage{tikz}
\usepackage{scalerel}
\newcommand{\SDelta}{\scalerel*{%
\tikz{\draw (0.2,0) coordinate (RBASE) --(0,0) coordinate (LBASE) --++(45:0.32) coordinate (TOP) --cycle;
\draw [line width=0.25mm] ([xshift=-0.01cm]RBASE)--([xshift=-0.01cm,yshift=-0.015cm]TOP);
\draw ([yshift=0.005cm]RBASE)--([yshift=0.005cm]LBASE);
}}{\Delta}}
\begin{document}
\[
\SDelta J = \int_{t_0}^t \SDelta F \, \mathrm{d}t
\]
\[\scriptstyle
\SDelta J = \int_{t_0}^t \SDelta F \, \mathrm{d}t
\]
\[
\Delta J = \int_{t_0}^t \Delta F \, \mathrm{d}t
\]
\[\scriptstyle
\Delta J = \int_{t_0}^t \Delta F \, \mathrm{d}t
\]
\end{document}
stixfont (Also available in OpenType as XITS Math) a slanted\mathit{\Delta}that looks much like this. It is, however, a relatively thick font. Inunicode-math, you can also\setmathfontwith therange=\mitDeltaandFakeSlantoptions. – Davislor Aug 31 '18 at 03:36\mitDelta, and might be a better match for the weight of your other fonts. So, perhaps\setmathfont[range=\mitDelta, Scale=MatchUppercase]{Cambria Math}after your primary\setmathfont. – Davislor Aug 31 '18 at 03:38