Most probably you have waveform compression enabled and the compression algorithm has too high a relative tolerance to process such a signal correctly, since the AC component is so small compared to the DC offset.
Open the control panel and decrease the relative tolerance:
LTspice usually performs waveform compression to avoid generating huge data files for waveforms. The compression algorithm is lossy, so you might lose details and have artifacts like those you see on your simulation.
LTspice online help excerpt:
LTspice compresses the raw data files as they are generated. A compressed file can be 50 times smaller than the un-compressed one. This is a lossy compression. This pane of the control panel allows you to control how lossy the compression runs.
Sometimes it is useful to disable compression entirely, for complex waveforms, but expect GB size .raw files (these are the files where LTspice saves waveform data). Neverthelss, usually it is sufficient to play around with compression settings, but only when you reasonably know what to expect from a simulation.
EDIT (to address some relevant comments)
Some commenters have pointed out that increasing tolerances, or specifically,
reltol SPICE parameter will increase simulation time. This is true, but compression
relative tolerance has nothing to do with the
reltol SPICE parameter, which is found in another tab of the control panel:
To further reinforce my point, I'll cite the whole section of LTspice's help concerning the
compression tab of the control panel (emphasis mine):
LTspice compresses the raw data files as they are generated. A
compressed file can be 50 times smaller than the un-compressed one.
This is a lossy compression. This pane of the control panel allows you
to control how lossy the compression runs.
Window Size(No. of Points): Maximum number of points that can be
compressed into two end points.
Relative Tolerance: The relative error allowed between the compressed
data and the uncompressed data.
Absolute Voltage tolerance[V]: The voltage error allowed by the
Absolute Current tolerance[A]: The current error allowed be the
These compression settings are not remembered between program
invocations to encourage use of the defaults. They are available on
the control panel for diagnostic purposes. The tolerances and window
size can be specified with option parameters plotreltol, plotvntol,
plotabstol and plotwinsize in .option statements placed as SPICE
directives on the schematic.
You will probably want to turn of compression when using .four
statements or doing FFT's in post analysis of your data with the SPICE
Again, the last directive just amounts to disable compression as you would do using the control panel. As I've already said above, this is just what you want to do to avoid artifacts, but huge files will be generated.