Here's a workaround. You can set the axes' TitleHorizontalAlignment property to left and the title's VerticalAlignment property to Top.
polarplot(rand(1,10),rand(1,10));
Ax = gca;
Ax.ThetaZeroLocation = 'bottom';
Ax.ThetaLim = [270 360+90];
Ax.LineWidth = 2;
Ax.FontSize = 16;
Ax.FontWeight = 'bold';
Ax.RLim = [0 1e-7];
Ax.ThetaTick = Ax.ThetaLim(1):10:Ax.ThetaLim(2);
Ax.RTick = Ax.RLim(1):1e-8:Ax.RLim(2);
Ax.ThetaTickLabel = compose('%d',-90:10:90);
% Workaround:
t = title('Title','FontSize',20,'FontWeight','bold');
Ax.TitleHorizontalAlignment = 'Left';
t.VerticalAlignment = 'top';
Alternatively, use tiledlayout
Tiledlayout uses a different space management system. This demo manually inserts newline characters to break up the long title.
figure('position',[50 50 600 600])
tiledlayout(1,1,'padding','compact')
Ax = nexttile();
polarplot(rand(1,10),rand(1,10));
Ax = gca;
Ax.ThetaZeroLocation = 'bottom';
Ax.ThetaLim = [270 360+90];
Ax.LineWidth = 2;
Ax.FontSize = 16;
Ax.FontWeight = 'bold';
Ax.RLim = [0 1e-7];
Ax.ThetaTick = Ax.ThetaLim(1):10:Ax.ThetaLim(2);
Ax.RTick = Ax.RLim(1):1e-8:Ax.RLim(2);
Ax.ThetaTickLabel = compose('%d',-90:10:90);
% Workaround:
str = ['I want this',newline(),...
'chart title to',newline(),...
'be wholly visible',newline(),...
'in the top-left',newline(),...
'hand corner of',newline(),...
'the screen'];
t = title(str,'FontSize',20,'FontWeight','bold');
Ax.TitleHorizontalAlignment = 'Left';
t.VerticalAlignment = 'middle';
t.HorizontalAlignment = 'left';
